enigmatic puzzle - Who stole the diamond?

_{Inspiration from @BeastlyGerbil's Puzzle - This is an opprtunity. Can you take it?}

---

In Puzzlville last night, someone stole the famous Stone of Wondrous Mystery!

Can you help the police find it? But first... maybe you should read the news.

_{Note: I cannot confirm that all of the images came through clearly enough. If you find that there's something that you can't... read, then let me know, and I can supply the original image that you can't read... probably.}

Hint:

There's a reason that there's one dark green and one light green in each sudoku box. Also, I made a mistake - foe should be for.

Answer

Final Complete Answer:

---

The original image QR gives:

Charles = Kyle

Clicking on the image and reading the QR there gives

vavqvny=qrnz (@Deusovi points out this is rot13 for initial=team)

Notably it's upside down

The barcode on the cereal says:

cereal

And the QR says:

irving=corey

The barcode on the side gives

E5vEw.png

a link to here

The QR there says:

casper is actually jon. jon skeet. heh heh heh. just kidding. but he's really jon.

The barcode there says:

bart=j.a.

there is also a hidden imgur address

'aayEK.png'

which leads to:

The solution to the sudoku is:

The light green tiles give:

418862151

The dark green tiles give:

131399235

The suspects as listed below give their stories:

Charles Kyle Hendricks (26) Chicago Cubs Pitcher - Last night, I was out late at the Sphinx's bar, drinking with my buddies. Then at 'round midnight, I staggered off home, you know, at 28 Enigma Road. You can check with my buddies if you want.

Wesley Roak Tanner Roark (34) Washington Nationals Pitcher - I was just too tired to go to the game, I was sleeping. I haven't been anywhere near that museum. It's full of boring strange things - why would I go there?

Casper Lester Jon Lester (29) Chicago Cubs Pitcher - I was out of town last night, visiting my pop in Yhpargonagets [Steganography backwards]. I didn't touch no diamond.

Irving Kluber Corey Kluber (31) Cleveland Indians Pitcher - could not be found

Bartholomew J. Happ James Anthony Happ (37) Toronto Blue Jays Pitcher - could not be found

@Mithrandir has said Dark green then Light green so

131399235418862151

there is also another imgur link

leading to:

That has a link

to

The bear from sesame street

From this @Scimonster correctly deduced

That the baseball pitch and a baby bear indicates the CUBS

So the culprit is either Kyle Hendricks or Jon Lester

It has been repeatedly said Dark the Light so:

You will notice that each cell in the Sudoku has 1 dark green and 1 light green. The dark green number indicates the line number in the newspaper, the light green represents the letter. I'll edit in each line in a second. (Thanks @Scimonster)

Using this we get

1. Dark = 1 Light = 4 - Last night, under cover of
2. Dark = 1 Light = 8 - Last night, under cover of
3. Dark = 3 Light = 1 - broke into the Museum - Mistake
4. Dark = 9 Light = 6 - Mystery. Upon arriving
5. Dark = 3 Light = 8 - broke into the Museum
6. Dark = 9 Light = 2 - Mystery. Upon arriving
7. Dark = 5 Light = 1 - founded by the Commitee
8. Dark = 2 Light = 1 - of darkness, someone
9. Dark = 3 Light = 5 - broke into the Museum - Mistake

thbrtyfoe

However @Mithrandir says in the hint that 'foe' should be 'four'. There also seems to be another error. It should actually be

Thirty Fo(u)r

Which is

Jon Lester's Shirt Number

So the thief is

Jon Skeet Jon Lester

strategy - Where are the Wazirs?

A wazir is a fairy chess piece that moves like a rook, but can go only one square.

                                                              

We wish to place a number of wazirs on a 9 $\times$ 9 chessboard so the following conditions are satisfied

1. Each wazir is being attacked by at least one other wazir.


2. Each empty square is being attacked by at least one wazir.

What is the minimum number of wazirs we need to place to satisfy the conditions above?

Answer

I have a solution with

25 wazirs:

Step by step:

We can cover all border squares with 8 pairs of wazirs whose attacking squares do not overlap. Note that each wazir covers two border squares, which is the maximum because it's not possible for a piece to be orthogonally adjacent to 3 border squares on a 9x9 board. So there is no way to cover the entire border with fewer wazirs.

Also note that this arrangement covers the maximum amount of non-border squares as well. Every wazir covering two border squares covers exactly one non-border square, unless it is located one step diagonally from a corner (in which it covers 2). Every square one step diagonally from a corner is in use, so the wazirs cover the maximum possible amount of non-border squares.

There are 17 dark squares left, so we need a minimum of 5 wazirs to cover them all.

Then we need four more wazirs to cover the remaining 12 light squares.

logical deduction - Who committed the crime?

A crime has been carried out by one person, there are 5 suspects. Each suspect is asked under polygraph who they think committed the crime.

Their answers are as follows:

• Terry : It wasn't Carl, It was Steve



• Steve : It wasn't Matt, It wasn't Carl


• Matt : It was Carl, It wasn't Terry


• Ben : It was Matt, It was Steve


• Carl : It was Ben, It wasn't Terry

The polygraph showed that each suspect told one lie and one truth. Who committed the crime?

Answer

Answer:

Matt.

Reasoning:

"Ben : It was Matt, It was Steve". So it has to be Matt or Steve.
If it would be Steve then Terry would tell the truth twice (It wasn't Carl, It was Steve).
Hence, it was Matt.

And it fits the requirement of one truthful answer and one lie for each.

Terry : It wasn't Carl (T), It was Steve (F)

Steve : It wasn't Matt (F), It wasn't Carl (T)
Matt : It was Carl(F), It wasn't Terry(T)
Ben : It was Matt(T), It was Steve(F)
Carl : It was Ben(F), It wasn't Terry(T)

visual - What number is hidden in this gallery?

This is another chapter from the puzzle crime series I am running on my website (you can find two previous puzzles here and here). I asked a real artist to make the illustration for this one and thought it turned out very pretty, so decided to share.

The goal is to find a passcode which is a 4-digit number.

7. The Third Body

Fifteen minutes later Morrow, Flanders, as well as three other police officers were in front of the former mayor’s house. It was a large building, with its own parking lot, a fountain, and everything you could expect from an expensive, luxurious mansion. The five men tried to call Phil one last time and when nobody answered, they broke the door. It didn’t take them long before they found him lying dead in the Claptons’ personal gallery room. He was holding a red rose in his hands.

P.S. The text is mostly to drive the story, focus on the illustration.

P.S.S. I simplified the puzzle a bit - initially the letters on the left spelled "Love".

Answer

The number hidden in the picture is:

3274

Explanation: After the simplification in the question (the original one featured the word "LOVE" instead of "LUST") this is what I get...

...turning upside down the 12x5 panel on the front wall, then using the word LUST as a XOR mask for it:

This is...

... the 12x5 panel, turned upside-down:

This is the word I used as...

... XOR mask:

...and the result of the...

... XOR operation is:

the number 3274

Deeper explanation:

The pictures on the left wall suggest you must "put a 4 letters word on top" of the picture on the front wall. The first picture on the right suggest that you must turn white those squares where 2 black squares take place.
The second picture on the right gives a hint on turning upside down the 12x5 panel and on using a word in opposition to LOVE (the word used in the original question instead of LUST)

36-length snake in a 6x6 grid

Based on https://brilliant.org/weekly-problems/2017-05-29/advanced/?p=4

We need to fill a 6x6 grid using the numbers 1-36, each cell having a single unique number, such that:

• Every two consecutive numbers lie in cells that share an edge.


• No two cells that share an edge or a vertex exist that both contain multiples of 4.

I found a solution for this. Highlighting the cells with multiples of 4 gives

x x x x x #
# x # x x x
x x x x x #
# x # x x x
x x x x x #
# x # x x x

as pointed out by a user there. Can someone prove why any valid solution to this question causes the multiples of four to form the above arrangement, or else find a solution where they don't.

P.S. Consider looking at the solution to the original question first.

Answer

Yes, this solution is unique, except obviously for mirroring and rotations.

Now the explanation is a bit long and not spoilered, proceed at your own risk. There might be a simpler formulation too.

We can safely ignore odd numbers and consider just even ones for now. We get a checkerboard pattern. We can easily see that half of the pattern is multiple of just 2 (not 4) and other half is multiple of 4 = 9 each. Now we need to place those multiple of 4 in such a way they don't touch diagonally. Lets consider 2 rows at a time, and in those rows just the checkerboard spots. So in the first 2 rows you have 6 spaces for 4 or 2. You can easily see you cannot fit more than 3 of 4, so you need to fit 3 to squeeze in all 9 in these 3 pairs of rows.

There are just 2 distinct options you have (note that 4 above prevents 4 down and down-right):

1:

4 4 4
2 2 2

2:
2 2 4
4 4 2

(there are also 2 4 4; 4 2 2 and 2 2 2; 4 4 4, but end up being the same as 1 and 2)

Now repeat this 3 times. This time 4 above prevents it down and down-left. Pretty obviously if you pick pattern 1 on top you can continue with either of 1 or 2; 2 can be continued by 2. So you end up with the following possible sequences for the rows:

111, 112, 122, 222

On the quick glance it seems just 111 and 222 are really distinct. 222 was proposed as the solution. Can we make it work with 111 too? Let's go back to the original square and mark 2s and 4s in it (.s are odd, which we continue ignoring).

.4.4.4
2.2.2.
.4.4.4
2.2.2.
.4.4.4
2.2.2.

We see that 4 must be preceded by 2 and followed by 2, except for one 4 which isn't followed by 2 - number 36. So, this last number needs to be in the top right corner, which has just one 2 that can be reached, which is then 34. OK, but now the problem is the middle 4 on the top and right. Both of those 4s have just one own 2 and share another 2 among them - the one with 34 on it. So you can make it work for one of them, not both. This means you cannot put 4s in the 111 pattern.

english - Double Speak - Phrases that need rewording

Each of these phrases can be reworded into a Double Speak phrase. A Double Speak phrase has two homophones together in the same phrase. For example a "Warrior's time of rest" could also be called a "Knight's Night". The thirteen phrases that need rewording are as follows:

• Unwarranted reversal.


• Untied rope.


• Cover up a detector.



• Reduce the education.


• Wedge of the clock belonging to us.


• Story about the end of a dog.


• Rabbit's fur.


• Deserve a pot.


• A pair of one-on-one battles.


• Find a purpose for some wood.


• Path taken by the bottom of a tree.


• Pilfer some metal.


• Curve on a boat.

Once you have found each of these 13 Double Speak phrases, look closely. There is a fourteenth phrase that needs rewording hiding somewhere. I'm looking for this 14th Double Speak phrase; it is the final solution to this puzzle.

Answer

Unwarranted reversal.

Undue undo

Untied rope.

Not knot.

Cover up a detector.

Censor sensor

Reduce the education.

Lessen lesson

Wedge of the clock belonging to us.

Our hour

Story about the end of a dog.

Tail tale

Rabbit's fur

Hare hair

Deserve a pot.

Earn urn

A pair of one-on-one battles.

Dual duel.

Find a purpose for some wood.

Use yews

Path taken by the bottom of a tree.

Root route.

Pilfer some metal.

Steal steel

Curve on a boat

Ark arc

The meta is given by:

The first letters: UNCLOTHED URSA

...which is of course,

Bare bear.

visual - Another new puzzle type needs a name

_{For an example of how this type of puzzle works, see here...}

---

I believe I have invented another new type of puzzle...

What is its name?

^{Colour-blind-friendly version available here.}

Begin by solving the 9x9 sudoku; each of the digits 1-9 must appear exactly once in each row, column and thick-bordered 3x3 box. Then apply some grid-deduction-deduction (!) and discover its name!

Hint:

Its name is 8 letters long. Though you may be able to guess it, you'll need to explain how to derive it from the puzzle...

Answer

The name of this puzzle is

Yajidoku

I solved the Sudoku, then learned from the other answers here, that the next step is to solve a Yajilin, a puzzle type I haven't heard of before. As these both steps are already covered in the other answers, I only give the combined solution here:

Now the last step is

to sum up in each of the nine Sudoku blocks both the numbers colored initially and the numbers blackend for the Yajilin. The middle block has no such numbers, the other sums are, read clockwise (like the arrows indicate) starting top left*:
25, 1, 10, 9, 4, 15, 11, 21
mapping this on 1-26 = a-z gives:
YAJIDOKU

*Addition:

If we order the colours as they appear in the rainbow from the outside to the inside, we have red - yellow - green - blue, which hints to start reading top left.

logical deduction - Dissect a square into 3:2 non-congruent integer-sided rectangles

(Similar to the recent 3:1 rectangle question)

Tile a square completely with rectangles which have aspect ratio 3:2, integral side lengths and all different sizes. In other words selected from 2x3, 4x6, 6x9 etc. Usual tiling rules apply: No gaps, no overlaps.

1. Find the smallest area tiling.


2. Find the tiling with with the fewest rectangles.

I have no way of proving that my answer to (1) is an answer to (2), so you could supply that proof in lieu of a tiling with fewer rectangles. Without such a proof, (2) is open ended - you could conceivably have a square one million units on a side tiled with just a handful of rectangles.

I've tagged this computer-puzzle, but I would not be surprised if it could be found by hand with a healthy dose of logic. So I also tagged it logical-deduction, but I would guess part (1) is easier with computer for most people. Part (2) requires a logical proof in order to not be open ended.

I found this by computer, a brief Google search didn't turn up any existing work in the area but it could still be a known problem.

Answer

My primitive and awfully slow program found this solution for part 1 of the question:

Size: 120; Rectangles: 10

The code:

package puzzle;

import java.util.ArrayDeque;

import java.util.BitSet;
import java.util.Deque;

public class Dissector {
    private static class Rectangle {
        public final int width;
        public final int height;
        public final int x;
        public final int y;


        public Rectangle(int width, int height, int x, int y) {
            super();
            this.width = width;
            this.height = height;
            this.x = x;
            this.y = y;
        }

        public boolean overlap(int width, int height, int x, int y) {
            return this.x < x + width && x < this.x + this.width  &&

                    this.y < y + height && y < this.y + this.height;
        }

        @Override
        public String toString() {
            return width + "x" + height + "+" + x + "+" + y;
        }
    }

    private final int width;

    private final int height;
    private final int factorWidth;
    private final int factorHeight;

    private int areaLeft;
    private final BitSet notPlaced = new BitSet();
    private final Deque placed = new ArrayDeque<>();

    public Dissector(int width, int height, int factorWidth, int factorHeight) {
        this.width = width;

        this.height = height;
        this.factorWidth = factorWidth;
        this.factorHeight = factorHeight;
        this.areaLeft = width * height;
        for (int i = Math.max(width, height) / Math.max(factorWidth, factorHeight); i > 0; -- i) {
            notPlaced.set(i);
        }
    }

    private boolean place(int recId, boolean rotated, int x, int y) {

        int recWidth = (rotated ? factorHeight : factorWidth) * recId;
        int recHeight = (rotated ? factorWidth : factorHeight) * recId;
        if (x + recWidth > width || y + recHeight > height) {
            return false;
        }
        for (Rectangle r : placed) {
            if (r.overlap(recWidth, recHeight, x, y)) {
                return false;
            }
        }

        placed.addFirst(new Rectangle(recWidth, recHeight, x, y));
        return true;
    }

    public void dissect(int startX, int startY) {
        if (areaLeft == 0) {
            System.out.println(placed);
        } else {
            int x = startX;
            int y = startY;

            boolean moved = true;
            while (moved && y < height) {
                moved = false;
                for (Rectangle r : placed) {
                    if (x >= r.x && x < r.x + r.width && y >= r.y && y < r.y + r.height) {
                        x = r.x + r.width;
                        if (x >= width) {
                            x = 0;
                            ++ y;
                        }

                        moved = true;
                        break;
                    }
                }
            }

            if (y < height) {
                int recId = notPlaced.length();
                while ((recId = notPlaced.previousSetBit(recId - 1)) > 0) {
                    notPlaced.clear(recId);

                    areaLeft -= recId * recId * factorWidth * factorHeight;
                    if (areaLeft >= 0) {
                        if (place(recId, false, x, y)) {
                            dissect(x, y);
                            placed.removeFirst();
                        }
                        if ((x > 0 || y > 0) && place(recId, true, x, y)) {
                            dissect(x, y);
                            placed.removeFirst();
                        }

                    }
                    notPlaced.set(recId);
                    areaLeft += recId * recId * factorWidth * factorHeight;
                }
            }
        }
    }

    public static void main(String[] args) {
        for (int size = 6; size < 200; size += 6) {

            System.out.println("size: " + size);
            Dissector splitter = new Dissector(size, size, 3, 2);
            splitter.dissect(0, 0);
        }
    }
}

wordplay - Venetian word pairs — part 2

A previous posting introduced the concept of Venetian word pairs. Relaxing the rules a bit opens a whole new world of Venetian word pairs.

Let's allow the transformation to use sections which may consist of a single letter. Obviously, the reversal of a single letter is just itself again.

So SORCERESS becomes RECROSSES:

1. SORCERESS
2. SORCER ES S
3. RECROS SE S
4. RECROSSES

The hint for the above might be something like:

female wizard

<===> The tiger continually _________ his territory in search of prey and intruders

Now see how many of the below you can solve:

1.  a fan of Peter, Ivan, Nicholas, Catherine, and all the rest
    <===>  Dire _______

2.  ______ the number until the call goes through
    <===>  Emergency!  We've had a train ______

3.  Can you believe that people used to carry these fireworks around in their cars

    in case of emergency?
    <===>  more wrong than wrong

4.  no clothes
    <===>  clothes are scattered all over the floor

5.  Why, Mrs. Winthrop, you're looking quite ______ this evening!
    <===>  ______ball

6.  In youth, heights increase.  In middle age, ______ increase.

    <===>  Bill of ______

7.  The longer the baby goes without a nap, the _______ he becomes
    <===>  a split

8.  big dog patrols the ski slopes
    <===>  marketers' reset

9.  Applaud all you want, this orchestra never comes back out for _______
    <===>  Surgeons removed the tissue before it started to _______


10.  The battlefield was strewn with _______
     <===>  creative _______

11.  mathematical shape with infinite complexity
     <===>  boxcar train or _______ train

12.  calm
     <===>  seen again


13.  anything relating to marriage
     <===>  If you can braid hair then you can also undo the braids

14.  six-legged animal
     <===>  She's the ______ person I've ever met!

15.  often found in a fireplace holding the coals
     <===>  very weird

16.  edible shellfish

     <===>  it can't be added up

17.  get back together again
     <===>  known more commonly as a posse or an entourage

18.  This ______ some interesting questions
     <===>  comes up

19.  The British press ________ Winston Churchill
     <===>  Hand lotion leaves a feeling of ________ that I dislike


20.  To smooth down this rough wood, you'll need a ______
     <===>  caught in a net

21.  all the ceremonial stuff around royalty
     <===>  the price of sending goods by train

22.  This extravagant staircase is even _______ than the last!
     <===>  unusual word for snarled


23.  Interest _______ in a bank account
     <===>  to put a witchy spell on

24.  one after the other
     <===>  If you enjoyed sailing it the first time then why not again?

25.  He's not just a pastry chef, he's a true ______
     <===>  Some ______ you're just born with

26.  They don't appreciate my dirty jokes because they're all a bunch of ______

     <===>  lips were pressed together tightly

27.  Maybe I really ought to tone down the ________ of my jokes
     <===>  I guess if you can have several kinds of old laces then you can also have several kinds of ________

28.  This tropical drink is made with ______ of mango, papaya, and guava
     <===>  to read very carefully

29.  a place to store your clothes
     <===>  obscure carpentry term relating to the hole drilled for pinning a mortise-and-tenon joint

---

Unsolved: 7, 19, 22 All have been solved

Answer

FINAL ANSWER with much help from @Nicolas Budig and @JohnMark Perry

1 (@Nicolas Budig):

TSARIST <-> STRAITS

2 (@Nicolas Budig):

REDIAL <-> DERAIL

3:

FLARES <=> FALSER

4 (@JohnMark_Perry):

NUDITY -> NU DIT Y -> UN TID Y -> UNTIDY

5:

LOVELY <=> VOLLEY

6:

GIRTHS <=> RIGHTS

7:

FUSSIER <=> FISSURE

8:

BERNARD <=> REBRAND

9:

ENCORES <===> NECROSE

10 (@Nicolas Budig):

CORPSES <-> PROCESS

11:

FRACTAL <=> FLATCAR

12:

SERENE <=> RESEEN

13:

NUPTIAL <=> UNPLAIT

14 (@Nicolas Budig):

INSECT <-> NICEST

15:

BRAZIER <=> BIZARRE

16 (@JohnMark_Perry):

MUSSELS -> MUS SEL S -> SUM LES S -> SUMLESS

17 (@Nicolas Budig):

REUNITE <-> RETINUE

18:

RAISES <=> ARISES

19:

OILINESS <=> LIONISES

20:

SANDER <=> SNARED

21 (@JohnMark_Perry):

REGALIA -> R EGALIA -> R AILAGE -> RAILAGE

22:

GRANDER <=> GNARRED

23 (@Nicolas Budig):

ACCRUES <-> ACCURSE

24:

SERIAL <=> RESAIL

25 (@JohnMark_Perry):

ARTIST -> ART I ST -> TRA I TS -> TRAITS

26:

PRUDES <=> PURSED

27:

RACINESS <=> ARSENICS

28:

PUREES <=> PERUSE

29 (@JohnMark_Perry):

WARDROBE -> WARD ROB E -> DRAW BOR E -> DRAWBORE

mathematics - The Number Kidnapper

I was just walking around with my friends Derek, Alice, and Peter, when suddely, WE WERE KIDNAPPED!

We were driven away in a van to a secret hideout, where we met our kidnapper. He calls himself Robert.

"Now listen closely," he said. "I'll let you guys go if you can guess your number. My number is 78."

We agreed, since we really had no other choice.

"All right. Derek, you go first."

Derek seemed scared that the kidnapper knew his name, but he calmed down, and guessed 43.

"That's right! You can go. Alice?"

Alice asked how much time we had. "All the time in the world, my dear."

Alice thought about it for a few minutes, and guessed 30.

"Right again! You can go too. Peter, what's your guess?"

Peter sat there and stammered. "Um, 17?"

"Wrong! You thought your numbers would be in a pattern, but they aren't! There's a code, something the other two must've realized. Guards! Take him to the dungeon."

The guards hauled him off to the dungeon. "His number was 64. Now, ASCIIThenANSI, what's your number?"

I only get one shot before I'm thrown in the dungeon, and you gotta help me!

What's my number, and why?

Answer

Your number is

131

The numbers are

The sums of each letter's position in the alphabet

That is:
ROBERT = R + O + B + E + R + T = 18 + 15 + 2 + 5 + 18 + 20 = 78
DEREK = D + E + R + E + K = 4 + 5 + 18 + 5 + 11 = 43
ALICE = A + L + I + C + E = 1 + 12 + 9 + 3 + 5 = 30
PETER = P + E + T + E + R = 16 + 5 + 20 + 5 + 18 = 64

so your number must be

A + S + C + I + I + T + H + E + N + A + N + S + I =
1 + 19 + 3 + 9 + 9 + 20 + 8 + 5 + 14 + 1 + 14 + 19 + 9 = 131

puzzle creation - Guessing among 3 possibilities with a single question - can this be done with letters as well as numbers?

This is an open question to all.

I have seen a few " I am thinking of a number/s-- can you guess by asking one question to which I can only answer Yes, No or may be" puzzles which are interesting from logic perspective.

Are there similar puzzles that talk about Letters instead of numbers?

If not can one design a hard puzzle ( I am thinking of letters L,M or N just as an example) and have a defined solution?

If this type of puzzle already exists then I am sorry for this question. I could not find it.

cipher - Which door leads to freedom?

You wake up in a room. In front of you, there is some paper:

It's the day, not the year or the month! It's very useful to abecedarians. 639407344. But never forget the time, for its another key.

Jsz amxroc tt ioatblq gstk A.

There are also 26 doors, labeled A through to Z. One door leads to freedom while the others lead to a pit of acid.

Which door should you go through?

HINT 1:

He jumped on the number! UNIX!!!

HINT 2:

The word 'abecedarian' is used to describe a person that is learning the alphabet.

HINT 3:

There are no clues as to which cipher is used, so you've got to work that out from the keys. If the time is a key, then that is presumably a number. And the used cipher is similar to a Vigenere cipher. Anything come to mind, cryptologists?

HINT 4:

The only important part of the word 'abecedarian' is the meaning. A person who is learning the alphabet.

Answer

As Cristian Marian figured out, the number 639407344 is

The time/date Fri, 06 Apr 1990 13:09:04 GMT.

The question says that the day is very useful to abecedarians, which means that

The day (Friday) is going to be our alphabet key for our cipher.

Since we have the time (which is a number) as a second key, we know we're using

A Gronsfeld cipher, which is like a Vigenere but uses a number key instead of a letter key alongside the modified alphabet.

Putting it all together,

We input the cipher text with an alphabet of FRIDAYBCEGHJKLMNOPQSTUVWXZ and a key of 130904, giving us the result "You should go through door F".

So, I think I'll head through

Door F, of course!

mathematics - Wait wait wait wait... 1=0?

Wasn't quite sure if this was suitable for Puzzling; however it has a problem/puzzle in it, so decided to give it a shot. Please appropriately downvote if you feel you should.

Yesterday morning I came to class as usual, and a student came up to me. He said he had a proof that could revolutionize mathematics.

Being a Grade 11 teacher, I didn't believe him.

So I asked him to tell me about the proof, he said "I've divided it into several steps, and said it seemed to work perfectly well, with zero problems." Then he told me "It's a proof that 1 is equal to 0."

So I asked if he could find any mistakes, he responded "None that I could find, sir, however it wouldn't surprise me if there was. I had thought of it after you taught us factoring. I think you'd like to take a look".

I indeed did, and he showed me, mentioning that it was indeed stating $1=0$.

Obviously this is false, and by looking at the paper I noticed his trivial error almost immediately.

Assume x and y are two nonzero numbers.
$x = y$
$x^2 = x*y $
$x^2 - y^2 = x*y - y^2 $
$x + y = y $
$2*y = y $
$2 = 1 $
$1 = 0$

However, I have a challenge for you, and this is to find the error my student made.

But not only that, you must explain how everything he told me was true.

Answer

The errors lies here:

There is an implicit division by 0 between steps 3 and 4. Step 3 states: $x^2-y^2=xy-y^2$. Factoring this produces $(x+y)(x-y)=y(x-y)$. Going to step 4 requires that you divide through by $(x-y)$, but step 1 implies that $x-y=0$.

He is technically correct in what he said because:

He said the proof has "zero problems". This is correct; there is a problem with the number 0 in his proof.

mathematics - Generalization of Sum and Product puzzle

I heard from a clever person that for the problem mentioned before: I don't know the two numbers... but now I do a solution exists even if we change 100 to infinity.

So the formulation would be next:

Two perfect logicians, Summer and Proctor, are told that integers x and y have been chosen such that $x>1$ and $y>1$. Summer is given the value x+y and Proctor is given the value x⋅y. They then have the following conversation.

Proctor: "I cannot determine the two numbers."
Summer: "I knew that."
Proctor: "Now I can determine them."
Summer: "So can I."

Given that the above statements are true, what are the two numbers?

I don't know whether it is true. Can you find the solution or prove that it doesn't exists? Can you find a general solution for any integer $N$ if we have limitation $x+y

reverse puzzling - Reassemble the riddles!

I'd just finished writing four short 4-line riddles, painstakingly making sure each line was correct, when a wind caught the slips of paper I'd been using to write on and blew them all over the floor. Quickly I picked them up again, but the order of them was lost. I'd written each line of each riddle on a separate slip, so that I could rearrange them if necessary, but now I regretted this decision. Some of the lines were repeated multiple times (I'd tried to be clever by writing overlapping riddles), and I was struggling to remember which lines could be put together into which riddle. Here are all the lines, in alphabetical order and without punctuation:

1. "A faithful friend"


2. "Contracted to love"


3. "I can wave to you"


4. "I'm bound to you"



5. "In most of the world"


6. "Living by nose"


7. "Through woe or joy"


8. "Which we may run down"


9. "Without hands at all"


10. "You can feel my salt"

Can you reassemble these lines to form four simple 4-line riddles, and solve them?

I'm unsure how hard this challenge is going to be. If it goes unsolved for a while, the first piece of information I'll add is which of the 10 lines are duplicated.

This is the first puzzle of this kind I've made, and I'm unsure how well it's going to work. All feedback welcome.

Answer

This was a lot of fun, I think the result might be:

1:

In most of the world
you can feel my salt
I can wave to you
without hands at all

-Ocean

2:

Living by nose
I can wave to you
without hands at all
A faithful friend
-Dog

3:

Contracted to love
Through woe or joy
I'm bound to you
A faithful friend
-Spouse

4:

Living by nose
Which we may run down
Through woe or joy
You can feel my salt
-Tears

riddle - Four Directions #7 - Where and what am I?

To the North, take a horse to find something delightful
To the West, a game piece that was tight with Paul
To the South, he can't smell, although he wasn't spiteful
To the East, you might see lavadeserticus crawl

Drink and be merry while you admire the floor

Where and what am I?

---

Four Directions #1
Four Directions #2

Four Directions #3
Four Directions #4
Four Directions #5
Four Directions #6 (by @PotatoLatte)

Answer

I believe that you are in the

House of Dionysus in Paphos, Cyprus?

To the North, take a horse to find something delightful

A famed horse, the Byerley Turk, was one of three horses to be forefathers to modern thoroughbred racing. The something delightful is Turkish Delight seems to indicate Turkey is to the North. Per @jafe, the horse refers to the Trojan Horse, and the fabled city of Troy is believed to be in Anatolia. Thanks, @jafe!

To the West, a game piece that was tight with Paul

A game piece in chess is the Bishop, @Gareth McCaughan found that there's a pun in the word "tight": the Titus to whom one of the allegedly-Pauline letters in the New Testament is addressed was the Bishop of Crete. Thanks, @Gareth! Crete is to the West.

To the South, he can't smell, although he wasn't spiteful

This could be the Sphinx (since he's missing his nose!) in Egypt, which is to the South.

To the East, you might see lavadeserticus crawl

This is the Syrian house gecko, endemic to Syria which must be to the East.

Drink and be merry while you admire the floor

At the entrance of the house is a floor made of shells depicting Scylla. Dionysus is also a God of drinking and being merry in the Greek pantheon.

riddle - Murder of the President - Part 4

This is Part 4 of the Murder of the President brainteaser/riddle series. If you have not already, check out the answers for Murder of the President - Part 1 posted by Nit and the answers for Murder of the President - Part 2 and Murder of the President - Part 3, both posted by Joe Z. Each part will give you a clue and you must solve it. Use all knowledge you have of cryptography, ciphers, past puzzles, etc. This question will have two different clues you have to solve. You should also use Google. This case is meant to take place in the present day, so all politicians, celebrities, places, etc. are who they are now. Please post your answers in spoiler tags.

---

Here's the riddle:

You arrive back at the White House at 11:18 p.m. EST. You go into the Oval Office and you begin searching the President's desk. All of the drawers are open and filled with paper work, except one. It is the bottom left drawer, not too big and it has a lock with three number codes, the first with two digits and the second and third with a four digit codes. You ask for the codes to the desk, but you are told that no one knew them besides the President. Weird, you think. You are given a piece of paper that has some clues that the President wrote that are the codes to the desk. Weird, you think once again. But you don't have time to worry about that now.

Here are the clues.

The first one seems to be a riddle.

Before you figure out this password
There is a riddle you must master
You must first get the tower that looms

Then you must find the hollow moon

---

The second one is just some words and letters that don't seem to make sense.

D.R.K Dahanu

---

The thirds seems to be a code.

Down the Rabbit Hole²

---

Once you manage to figure out the codes you open the drawer and, once again, you find a coded message.

Bl gl .l_cl_ QQI Z;;.D

---

What are the codes to the drawer? What does this coded message mean? Where should you go next?

Good luck

Hint:

APPLE is in all uppercase letters. It is not an address. The 118 is not as important as the London part.

---

Note: I will be posting Part 5 in one to two days. I will select the correct answer for Part 4 before, but I will post the answer for Part 4 if no one gets it

Answer

First numerical code is 10 (1 = tower, 0 - hollow moon, with credit to FortMauris for coming up with it first)

Second numerical clue is the Kaprekar constant: 6174

Lewis Carroll made frequent use of the number 42 in the novel Alice in Wonderland. 42^2 = 1764 for third number

There's a hotel called "The London" in downtown NYC at 151 West 54th Street. Presumably, it has a room number 118, so let's go there.

dissection - A spartan skeleton Sudoku

A skeleton crossword is a crossword where the black and white squares aren't given; you have to deduce them. Here's a generalisation of that idea to the Sudoku puzzle.

Here's a 4 by 4 grid, with four cells shaded:

(Just in case you can't see images, here's a text representation of that: I shaded the second cell on the first row, and all but the second cell on the second row.)

This is a generalised Sudoku grid; you need to ensure that each row, column, and region contains the numbers 1, 2, 3, and 4. Unlike a normal Sudoku (but like these two puzzles), the regions aren't necessarily square (however, like a normal Sudoku, the regions are contiguous, and each has a number of cells equal to the side length of the puzzle).

However, I haven't drawn the regions on the grid; you'll need to figure out what shapes they have for yourself. This works the same way as a Slitherlink: each clue specifies the number of edges of the square that are borders of regions (or equivalently, the number of adjacent squares that are either in different regions, or outside the grid).

As you can see by looking at the grid, I didn't draw the clues on the grid either. Rather, there are just those shaded squares. Each of the shaded squares contains a digit (1, 2, 3, or 4, although not necessarily one of each) such that it correctly clues both the shape of the regions of the Sudoku, and the number that goes in that square of the Sudoku. There's only one way to do it to make a solvable (generalised) Sudoku; not only that, the resulting puzzle also has a unique solution. What is the puzzle, and what is its solution?

Answer

No clue in the Slitherlink can be 4, as that would mean the square is isolated. So the clues on the second row are 1, 2, 3, in some order. Bruteforcing (see rand's answer for details on this step), we realize placing a 1 in either the first or second squares lead to the first row becoming isolated and not part of any regions, or containing two of the same number, so the only possibility is to place the 1 in the third square.

The rest is easier; 1 being the third clue forces the second clue in the second row to be a 3 due to the T-shaped tetromino, so the first square in the second row is a 2. This allows us to deduce the regions uniquely, and the resulting Sudoku is easy to fill:

pattern - What is a Perfect Word™?

_{This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.}

---

If a word conforms to a special rule, I call it a Perfect Word™.

Use the following examples below to find the rule.

Here is a CSV version:

PERFECT WORD™, NOT PERFECT WORD™
UNDERGROUND, SUBWAY
AFTERSHAFT, FEATHER
ENTERTAINMENT, AMUSEMENT
IONIZATION, NEUTRALIZATION

PHYTOGRAPHY, BOTANY
CALENDRICAL, PERIODICAL
REDECLARED, REASSIGNED
TORMENTOR, TORTURER
INGESTING, CONSUMING
RESTORES, REJUVENATES

Answer

A perfect word is

a word where the first three and the last three letters of the word are the same.

Example

und-ergro-und and aft-ersh-aft

How I found my answer

I first saw that every perfect wordt had at least twice the same two letter combination. After that I found out that it was a three letter combination at the start and end of the word.

Movie rebus puzzle

Here is an image containing rebus puzzles about movies.

Have fun solving it.

Answer

Top to Bottom, then Left to Right:

First Wives' Club
Dr. No
Last Tango In Paris
The Sweet Hereafter (Thanks @Khale_Kitha, I hadn't heard of that one)
Four Weddings and a Funeral
From Dusk 'Til Dawn
School of Rock
Brokeback Mountain

riddle - I have three fingers. What is this?

I have three fingers,

Middle finger has a triangle,

Left finger has a circle and,

Right finger has a square,

What is this?

Answer

It's­­­­­­­­­­­­­­

A USB icon.

mathematics - Hard 4x6 chocolate bar Riddle

You have the following 4x6 chocolate bar. The question is what is the least amount of cuts you have to do in order to create 24 pieces of 1x1 chocolates. the cuts can have any shape they want as long as they start from a point in the perimeter and end on another point of the perimeter. The line cant hit itself and every time we cut the chocolate we separate the pieces and cut each piece on its own.

mathematics - Island inhabitants: Who lies and who tells the truth?

On some island, the population is split into native people and into outlanders. There are more natives than outlanders.

Someone with extreme logical and mathematical thinking wants to know who are the strangers and who are the autochthons of this place, while asking as few questions as possible.

Feasible questions are:

• Are you a foreigner on this island?


• Is that dude a foreigner on this island?

Now .... we know that natives always tell the truth, whereas foreigners may lie whenever they want.

What is the minimum number of questions needed to find out who are the strangers and who are the autochthons on the island?

Hint:

the number works especially with big populations

mathematics - Baggage Problem: $1.5$-meter-long sword onto a train

This is the problem I came across reading the book The Art and Craft of Problem Solving. When I read this question I wasn't able to figure out the solution and I saw the solution after a while, but still I couldn't understand the solution as well.

Question:

Pat wants to take a $1.5$-meter-long sword onto a train, but the conductor won't allow it as carry-on luggage. And the baggage person won't take any item which greatest dimension exceeds $1$ meter. What should Pat do?

Solution:

This is unsolvable if we limit ourselves to two-dimensional space. Once liberated from Flatland, we get a nice solution : The sword fits into a $1 \times 1 \times 1$ -meter-box, with a long diagonal of $\sqrt{(1^2 + 1^2 + 1^2)}$ = $\sqrt{3} > 1.69$ meters.

Can anyone give me a clear explanation of this solution?

Answer

The sword fits in that 3D box, because the long diagonal is $1.69$ meter. The longest dimension of this box is 1 meter (length, width and height are all exactly 1 meter). The sword goes like the green line in the picture:

If Pat would use a flat case, it would be denied. In the most naive way, the box would be $1.5$ meter long and have a width of the sword itself. A more clever way to think is in the maximum dimensions, which are $1 \times 1$ meter. In that case the diagonal is $\sqrt{2} = 1.41$ meter long, which is not long enough. So the only option is to include the height into account.

rebus - ASCII Puzzler 2: Arrows Depicting Movement, Things, or Pointing Out Objects

This is a sequel to ASCII Puzzler 1: Part 1 and a prequel to ASCII Puzzler 3: The Trees and https://puzzling.stackexchange.com/questions/32439/ascii-puzzler-4-not-a-rebus.

Here is the second rebus I have for you to figure out:

 |
 V

---        O <---
 B --|--> -|-
---        /\
 ^
 |

Here is another rebus I made. The main theme of this is arrows.

Hint 1: (if you reword it, this is a major hint)

After that the B was flat.

Hint 2:

A hint to Hint 1: strike out 1, 2, 3, 5.

Answer

I hope this is wrong, but the answer could conceivably just be

B flat minor

on the grounds that

the person depicted is a miner (perhaps that nice round head is actually a miner's helmet) and he's got a flattened B attached to him. (And, er, "miner" and "minor" sound alike and "B flat minor" is a musical key.)

It seems unsatisfactory because

there is nothing in the puzzle that actually indicates that the person is a miner (or, I guess, a minor -- i.e., someone not yet legally adult), and all those arrows (featured so prominently in the title) end up not really signifying anything much

so I hope there's a better solution.

mathematics - Find the value of $bigstar$: Puzzle 1 - Evaluation

This puzzle replaces all numbers with other symbols.

Your job, as the title suggests, is to find what number fits in the place of $\bigstar$.

All symbols abide to the following rules:

1. Each symbol represents integers and only integers. This means fractions and irrational numbers like $\sqrt2$ are not allowed. However, negative numbers and zero are allowed.


2. Each symbol represents a unique number. This means that for any two symbols $\alpha$ and $\beta$ which are in the same puzzle, $\alpha\neq\beta$.


3. The following equations are satisfied (this is the heart of the puzzle): $$ \text{I. }\alpha\times\alpha=\alpha \\ \space \\ \text{II. }\alpha+\alpha=\beta \\ \space \\ \text{III. }\beta+\alpha=\gamma \\ \space \\ \text{IV. }\gamma\times\beta=\delta \\ \space \\ \text{V. }\delta\times\gamma=\varepsilon \\ \space \\ \text{VI. }\varepsilon-\beta=\bigstar $$

What is a Solution?

A solution is an integer value for $\bigstar$, such that, for the group of symbols in the puzzle $S_1$ there exists a one-to-one function $f:S_1\to\Bbb Z$ which, after replacing all provided symbols using this function, satisfies all given equations.

What is a Correct Answer?

An answer is considered correct if you can prove that a certain value for $\bigstar$ is a solution. This can be done easily by getting a function from every symbol in the puzzle to the correct integers (that is, find an example for $f:S_1\to\Bbb Z$).

An answer will be accepted if it is the first correct answer to also prove that the solution is the only solution. In other words, there is no other possible value for $\bigstar$.

Good luck!

Next Puzzle

Answer

I. α×α=α

The only values that satisfy this are 0 and 1

II. α+α=β

β=2α, but since 2.Each symbol represents a unique number, α and β both cannot be 0, so α=1 and β=2

III. β+α=γ

Plugging in our known values, γ=2+1=3

IV. γ×β=δ

Plugging in more values, δ=3*2=6

V. δ×γ=ε

Plugging in more values, ε=6*3=18

VI. ε−β=★

Plugging in more values, ★=18-2=16

Proof

This all relies on α=1
$$α*α=α$$ $$α*α-α=0$$ $$α^2-α=0$$ Using the quadratic formula... $$aα^2+bα+c=0$$ $$a=1, b=-1, c=0$$ $$α=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$ The two values for α... $$α=\frac{-(-1)+\sqrt{(-1)^2-4*1*0}}{2*1}=\frac{1+1}{2}=1$$ $$α=\frac{-(-1)-\sqrt{(-1)^2-4*1*0}}{2*1}=\frac{1-1}{2}=0$$ But since $β=2α$, and symbols are unique, α and β cannot be 0

wordplay - ''If the B...''

This is an ancient puzzle from an old book that I've never seen anywhere else. Can any of you puzzlers solve it?

If the B MT put:
If the B. putting:

Answer

If the grate be (great B) empty, put coal on (or maybe in?) (colon); if the grate be full stop putting coal in (on?).

logical deduction - Deaf, Mute and Blind

There were three men. One was deaf, the other was blind and the third was mute. One day the deaf man kissed the blind man's wife. The mute man saw this and he wants to tell it to the blind man, but he cannot speak. So how does the mute man explain the situation to the blind man.

Just to give a clarification regarding the question, I want to specify in detail these points: There were only three of them and the blind man's wife and no one else in the situation.

The mute man doesn't know how to write Braille.

logical deduction - A dozen into six rows?

You were given 12 coins by your friend. He bet that if you could arrange these dozen coins into 6 rows of 4 coins such that it makes two similar shapes, he will give you 12 more coins. How will you do it?

Answer

Forgive the badly drawn image:

Black are the coins, green are the rows of 4, red is the similar shape.

humor - The case of the world’s easiest puzzles

   Welcome back, my friends, to the show that never ends.   We’ re so glad you could attend,
   Come inside, come inside.
   Step inside, hello! We’ ve the least amazing show.   You’ ll enjoy it some, we know,
   Step inside, step inside.

   Rest assured, you’ ll get your money’s worth.   Easiest puzzles in Heaven or Hell or on Earth.
   If you follow me, to our speciality, real gimmes for you to see,
   Simplicity, simplicity.    — adapted from Karn Evil 9 _YouTube by Emerson, Lake & Palmer

Step right up to our traveling display case and be dumbstruck by the easiest puzzles you’ll ever see.

These abysmal abominations are so mind-numbingly vapid that we cannot even expose them to air, or they will spontaneously burst into solutions.   Ooo, you could swoon abashedly. Or you could shed all dignity and dare imagine just what it would be like to try and actually solve such crude puzzles, if permitted, quicker than they solve themselves.   Or, you could answer...

             What might each puzzle be anyway?

For instance, the first puzzle might be (though you should think of another)...

  a. World’s easiest paperfolding puzzle:   Divide into two areas by folding the fewest possible times.

Puzzle h has the special condition that its answer cannot also suit puzzle e.   Thus Knight’s Tour, for example, could be an answer only for puzzle e, which would be a 1×1 chessboard with a single white square, even though puzzle h could be perceived as an equivalent black square.

Only puzzles h, i and j are meant to be at all challenging to identify, the rest intended as warm-ups with room for playfulness. Some, certainly puzzle e, can represent countless of the world’s easiest puzzles.   Each puzzle is meant not only as the world’s easiest but also as the simplest, so special instructions should be minimal, or else some simpler puzzle is more likely the one represented.

$\small\sf\color{black}{Hints \! :}$   Some specimens are displayed at deliberately misleading scales.
    One of these sideshow geeks has a family member locked in The trunk of trivial trials.

Easier/simpler/additional samples, as improvements or new mysteries, are more than welcome!

Answer

Possible answers for the non starred ones:

a.

Symmetry puzzle: Fill in one square so the entire sheet has two lines of symmetry.

You

Fill in the middle square

b.

Its Haisu!

So

Draw a line through every cell from O to X

c.

Alphametic

So

What number could Z be? (Answer 0)

d.

Match puzzle: Move the match once to create a vertical line

e.

Division puzzle: Split the square into two triangles with one line (just draw a diagonal)

f

Its a cryptic clue

So

What the answer? (It's I)

g

Looks like tower of Hanoi

So

How many moves does it take to get the ring from L to R?

Now for the starred ones:

h

Could be a chess puzzle: How many squares can a knight reach from this square (0 as it's the only square)

It was actually:

A crossword. Solved by Gareth.

i

How about a keyboard puzzle? What other symbol is on this key on your keyboard (Answer +)

It was actually:

A maze. Solved by KeyboardWielder

j

Seems like a rebus. Don't know what it could be for though

Or (thanks @Silenus)

It is representative of a Droste effect of a puzzle in a puzzle in a puzzle

It was actually

Puzzle identification. Solved by Marius.

riddle - Large and in charge

Opened or closed, I continue to be.
A mechanism of choice, But I can be beastly.

I come in all shapes and sizes, Each with a common task.
I cling to life by a thread, What am I, I ask?

Added hint:

I can be made out of anything from A to Z, and sometimes have eyes with which I can't see.

Another Hint:

I hate to give another hint but there have been a ton of views and guesses, but here it is:
I have a few close friends, just like a pea, and I jump through hoops for everyone around me.

This is part 1 in a series by the way. The final part will use clues from each.

Answer

You might be:

a button

Opened or closed, I continue to be.

If you are buttoned up or not, you are still button.

A mechanism of choice, But I can be beastly.

Buttons are very often used, but some of them can be very tricky to unbutton.

I come in all shapes and sizes, Each with a common task.

Buttons come in all shapes and sizes, but they are all used to connect two pieces of clothing.

I cling to life by a thread, What am I, I ask?

Buttons are sown to clothes by a thread.

Hint 1:

I can be made out of anything from A to Z, and sometimes have eyes with which I can't see. Buttons can be made from many materials and they can have the holes for thread to be sown.

Hint 2:

I have a few close friends, just like a pea, and I jump through hoops for everyone around me. Buttons usually come in rows, like on a shirt. When you button up the shirt, you pass each button through an opening/hoop.

probability - Shooting Free Throws

Shaq is shooting free throws. He makes his first shot, then misses his second.

Confidence is a huge factor in how well Shaq plays. This means that for each subsequent shot, the probability he makes it is equal to the fraction of shots he has made so far.

For example, there is a $\frac12$ chance he makes his third shot. If he makes that, there is a $\frac23$ chance he will make his fourth.

After 101 shots (including the first two), what is the probability that Shaq sank less than 21 baskets?

^{Side note: Symmetry implies that Shaq will make half of his free throws on average, which matches his career average of 52.7% pretty closely.}

Answer

After $n$ shots, it is equally likely that Shaq has made any number of shots from $1$ to $n-1$.

Proof by induction:

If $n=2$, then Shaq has made $1$ shot, which is the entire range from $1$ to $2-1$.

Otherwise:

• For Shaq to make $1$ shot out of $n$, he must make $1$ shot out of $n-1$ and then miss the next shot. This has a probability of $\frac{1}{n-2}*\frac{n-2}{n-1}=\frac{1}{n-1}$.


• For Shaq to make $n-1$ shots out of $n$, he must make $n-2$ shots out of $n-1$ and then make the next shot. This has a probability of $\frac{1}{n-2}*\frac{n-2}{n-1}=\frac{1}{n-1}$.



• For Shaq to make $k$ shots out of $n$, with $1
  

So the probability that Shaq makes $m$ shots out of $n$, for $1\le m\le n-1$, is always $\frac{1}{n-1}$. The probability that Shaq makes between $1$ and $20$ shots inclusive out of $101$ is $\frac{20}{100}=\boxed{\frac{1}{5}}$.

Reverse Engineer These Five Ciphers

This is the latest material I have made for my Codes and Ciphers club. It involves showing both the ciphertext and the plaintext for messages using each of five ciphers alongside another ciphertext that uses the same cipher (the process and the key are identical).

1.1.1/GERAIHSCMASTISEETSES
1.1.2/RBOOTMYOOIKRYAFCE
1.2.1/this is a secret message
1.2.2/UNDEFINED/DIFF.3
2.1.1/RELOCATED

2.1.2/RELOCATED
2.2.1/we do not care for those people and their reckless sense of unchecked optimism
2.2.2/UNDEFINED/DIFF.3
3.1.1/XTVZMGBKVESQXYCEWGAYEMBRFWNMQEXYKMHJHKFZS
3.1.2/YMKPOQYYSZWPTRVLHUXPZOVGLRFUCETW
3.2.1/every time we deal with an enemy we create two more
3.2.2/UNDEFINED/DIFF.1
4.1.1/4423.1544.1532.3244.4415.1144.2315.3232.4412.5545.2315.4415.1144.2335.4315
4.1.2/3355.4435.3413.1132.3251.3353.1144.1235.4334.2434.3435.5215.3312.1543
4.2.1/she sells sea shells by the sea shore

4.2.2/UNDEFINED/DIFF.1
5.1.1/10100.11100.11201.22202.32213.32214.43215.44316.44417.55417.56418.56429.57540.67651.68652.69752.70852.80852.80853.91854.91964.93075.103085.104086.114186
5.1.2/110.1221.11321.12321.12322.12422.22533.22534.32545.42556.42657.43767.53867.63967.65078.75088.76199.86210.96221.97331.97432.108432.118532
5.2.1/they say mexico will pay for it
5.2.2/UNDEFINED/DIFF.2

Hint 1

Using the first cipher, "nothing beats waffles" becomes "sftgtonaaehnibsewfl".

Hint 2

Each "key" in the second cipher is meaningful, but not every part of each key is meaningful.

Answer

Cipher #1 (from @Gareth McCaughan's answer)

Solution:

I TOOK MORAY BY FORCE

Cipher #2 (from @Gareth McCaughan's answer)

Solution:

I WAS APPOINTED MARSHAL OF MORAY

For reasoning for the above two solutions, see Gareth's answer.

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Cipher #3

How to decipher:

It is a regular Vigenére cipher. We can try what is the key/passphrase being used by inserting the letters one-by-one until the prefix match. The key/passphrase for this one is "TYRION".

The secret message:

Fothad fabricated the rights to Moray.

Cipher #4

How to decipher:

Create this table:

A B C D E
F G H I J
K L M N O
P Q R S T
U V W X Y

Then for every two digits, it tells the pair of row and column. So, "4423.1544" is "SHES".

The secret message:

My son Callum was born in November.

Cipher #5

How to decipher:

If you separate each number by dots, try to subtract the next one with the previous one. So "10100.11100.11201.22202.32213" will result in "10100.1000.101.11001.10011".

After that, we can just decode the binary to number in alphabet, so "10100.1000.101.11001.10011" will be "THEYS".

The secret message:

Fothad was sent to Rossnext.

mathematics - Missing number in this sequence?

I heard this puzzle in a quiz I participated in:

10, 11, 12, 13, 14, 15, 16, 17, 20, 22, 24, ?, 100, 121, 10000

What is the missing number?

(You don't need to do any big calculations, and you don't need any advanced mathematical knowledge - just one basic concept that's known to many non-mathematical people.)

Answer

According the google the answer be 31.

The sequence is 16 in base 16-n.

no computers - Three for the price of one

While browsing through your local puzzle store, you see something you can't resist: a box which promises two grid deduction puzzles for the price of one!

The vendor explains that the box contains a single numbered grid depicting two uniquely solvable puzzles of different types. The types of puzzles vary from box to box but are specified in each box's instructions.

You fork over the meager sum of one upvote and rush home, giddy with excitement.

Unfortunately, when you arrive home and unbox the grid, you discover that not only does it require assembly, but also that the instructions are missing. All you find are four 2x2 squares which can be connected along their edges.

You feel certain that there is a unique way to combine them into a single grid on which can be played two puzzles of the intended types.

It dawns on you that assembling the grid is itself a puzzle. But that's fine with you—it means you actually got three puzzles for the price of one!

Answer

If we assume that one of the puzzles is a sudoku, we are left with only four possible grid constructions because the last two pieces can not be next to each other and have to form the diagonal. I tried slitherlink as the second puzzle which gave a unique solution for only one of those grids. In that grid the three corners with numbers can be solved immediately which quickly leads to the solution.

The solved sudoku then looks like this

There are probably other possible solutions depending on the chosen puzzles.

After trying lots of different puzzles, I might have to take that back. The only one that came close was a fillomino which had one grid with a unique solution if we forbid 4s.