Word Number Puzzle

If letters are factors of equations:

zero = 0

one = 1

two = 2

three = 3

four = 4

five = 5

six = 6

seven = 7

eight = 8

nine = 9

ten = 10

twelve = 12

fifteen = 15

twenty = 20

thirty = 30

forty = 40

sixty = 60

hundred = 100

thousand = 1000

million = 1000000

What is the product for answered = ?

Answer

The answer of the equation answered is

±3,401,222,400

Here I want to thank Matsmath to remind me that a negative solution do exist.

I use induction to find out the law behind the puzzle, with 11 steps below:

Step 1:

Let's take a look at sixty first. Here we can cut it into two pieces: six and ty. As six is known as 6, we can found that:

ty = 10

ten as 10, ty as 10, so there is a equation:

y = en

Then we can compare ty to other "tys". In forty we found:

for = 4

four as 4, also for as 4, so the letter u can be found as:

u = 1

In twenty we found that twen as 2, the same value as two, and another euqation is here:

en = o

Along with y = en we summarize that:

y = en = o In thirty, thir represent the value 3. Compare thir with three, we found that:

i = ee

Step 2:

Focus on one, and the equations we have in step 1:

y = en = o

Then we found the equation one can be seen as oo. Since the value is 1, we found that:

o = ±1

Then apply y = en = o with value o, we found:

y = en = o = ±1

Step 3:

Here we look at ten, with the fact that en is ±1, the value of t can be found:

t = ±10

Step 4:

Variable t has found, then we focus on equation two, along with the value of o, w is solved:

w = 1/5

Step 5:

Put equation en = ±1 into consider when we see nine, a new equation is found:

ni = ±9

Since ni need to multiply ne to have a positive 9, and we can assume that n could be a negative number.

Then combine i = ee with the equation above, we found that:

een = ±9

As we know en = ±1 and n can be negative, then e, n and i have been solved:

e = 9, n = ±1/9, i = 81

Step 6:

Back to equation thir, we join the value of t and i, and we found that:

81 * (±10) * hr = 3
27 * (±10) * hr = 1
hr = ±1/270

Step 7:

Take a look at hundred, here we join the value of u, e, and n (with both positive and negative), and:

hundred = hndrd = 100

We have found the value of hr in step 6, the equation become like this:

hndrd = hr * n * dd = (±1/270) * (±1) * dd = 100
dd = 27,000

Step 8:

For equation fifteen, put the value of i, t, e, n into it, and fifteen becomes:

fifteen = 81 * (±10) * 9 * (±1) * ff = 15

And ff is:

ff = 1/486

Then the f itself:

f = ±1/(9√6)

Step 9:

With the value of f, we can turn to four and solve r. First, join o = ±1, u = 1, we can see that:

four = f * (±1) * 1 * r

Then, join the value of f:

f * (±1) * 1 * r = ±1/(9√6) * (±1) * 1 * r
= 1/(9√6) * r = 4

And we can found r is (with square version):

r = 36√6
rr = 7,776

Step 10:

Move our step to thousand and hundred, we can apply a division here:

thousand / hundred = tosa / red = 1,000/100 = 10

Join t, o, and e s' value into it, and here it goes:

(±10) * (±1) * sa /9 * rd = 10
sa /9 * rd = 1
sa = 9 * rd

Step 11:

Finally, focus on the equation answered. Just a bit more to reach the solution!
Join the value of n, w, and e.

answered = a * (±1/9) * s * (1/5) * 9 * r * 9 * d

= (±1) * (1/5) * 9 * as * rd

We have known that as = 9*rd from step 10:

(±1) * (1/5) * 9 * as * rd = (±1) * (1/5) * 9 * (9 * rd) * rd
= (±1) * 81 * (1/5) * rrdd

Join the value of rr and dd from step 9 and 7 respectively:

(±1) * 81 * (1/5) * rrdd = (±1) * 81 * (1/5) * 7,776 * 27,000
= (±1) * 81 * 5,400 * 7,776

Note that there's a ±1 inside, and we found equation answered is actually:

answered = ± 3,401,222,400