Friday, 4 March 2016

logical deduction - Which lorry is carrying drugs?


Five lorries are parked in a French layby, having recently come off the ferry at Calais. The police know that the lorry headed for Lisbon is smuggling drugs, but they're not sure which one it is. All they have to go on is the following information.



  1. The Polish lorry came on the 6 o'clock ferry and is carrying coffee.

  2. The lorry in the middle is black.

  3. The British lorry came on the 9 o'clock ferry.

  4. The blue French lorry is somewhere to the left of the lorry carrying coffee.


  5. The lorry headed for Marseille is somewhere to the right of the lorry carrying potatoes.

  6. The Lithuanian lorry is headed for Nantes.

  7. The lorry carrying rice is next to the green lorry.

  8. The lorry headed for Genoa came on the 5 o'clock ferry.

  9. The Spanish lorry is somewhere to the right of the lorry headed for Marseille.

  10. The red lorry is headed for Hamburg.

  11. The white lorry is next to the Spanish lorry that came on the 7 o'clock ferry.

  12. The lorry carrying bread is at one of the ends.

  13. The black lorry came on the 8 o'clock ferry.

  14. The lorry carrying bread is next to the lorry carrying rice.


  15. The lorry headed for Hamburg came on the 6 o'clock ferry.


When the police arrive at the layby, which lorry driver should they arrest? I.e. should they raid the leftmost lorry, the second from the left, etc.?


Bonus question: which two possible lorries could be the one that's carrying tea?


In the spirit of teamwork, partial answers are acceptable.



Answer



Destination    Genoa     Hamburg    Nantes      Marseille   Lisbon
Origin French Polish Lithuanian British Spanish
Colour blue red black white green
Ferry Time 5 o'clock 6 o'clock 8 o'clock 9 o'clock 7 o'clock

Load ? coffee ? rice bread

The police should raid the rightmost lorry.


Bonus: The French and Lithuanian lorries could be carrying tea.


EDIT:


This is how I deduced the answer. Using the facts that I knew, I created two sets of lorries, the first using the positional information to determine the known places.


(Ordered set)
Destination
Origin
Colour (green) black (green)

Ferry Time 8 o'clock
Load (bread) (rice) (rice) (bread)

In the above, the bread load is at one of two ends (12) and rice is next to it (14), giving rise to two scenarios. The lorry carrying bread is green as it's next to the one carrying rice (7) and it can't be the one in the middle position as the middle lorry is known to be black (2) and it came on the 8 o' clock ferry (13).


In the second set, I used the remaining data to assign a set of possible characteristics to lorries.


(Unordered set)
Destination Hamburg Nantes Genoa
Origin Polish British French Lithuanian Spanish
Colour red blue
Ferry Time 6 o'clock 9 o'clock 5 o'clock 7 o'clock

Load coffee

The complete description of the Polish lorry is provided, barring the position (1,10,15). British lorry came in at 9 o'clock (3) and the French lorry is blue (4). The Lithuanian lorry is headed for Nantes (6) and the lorry to Genoa came in at 5 o'clock (8), while the Spanish lorry came in on the 7 o'clock ferry (11).


Looking at the second set, we can see that the nationality of the lorry to Genoa is the only one not known, but its time of arrival is known. There is only one other combination where both the nationality and time of arrival is missing, so I determined that the French lorry is headed to Genoa. Also, the timings for all are known except for the Lithuanian lorry, but I have the timing for the middle lorry, which is the one timing not accounted for.


(Updated ordered set)
Destination Nantes
Origin Lithuania
Colour (green) black (green)
Ferry Time 8 o'clock
Load (bread) (rice) (rice) (bread)


(Updated unordered set)
Destination Hamburg Genoa
Origin Polish British French Spanish
Colour red blue
Ferry Time 6 o'clock 9 o'clock 5 o'clock 7 o'clock
Load coffee

At this point, I was hard pressed to decide on a position for the lorry with bread. Let's consider I picked the leftmost position, then rice would be in the lorry at the second position. The lorry headed to Genoa would occupy the fourth position as it has to be on the left of the lorry carrying coffee (4). This means the lorry to Hamburg will be in the fifth position.


(Updated ordered set, invalid)

Destination Nantes Genoa Hamburg
Origin Lithuania French Polish
Colour green black blue red
Ferry Time 8 o'clock 5 o'clock 6 o'clock
Load bread rice coffee

However, this would violate the condition that the lorry headed for Marseille is somewhere to the right of the lorry carrying potatoes (5), since potatoes can only be in the last three positions (other two have bread and rice) and there I've determined the locations are Nantes, Genoa and Hamburg.


So consider that the rightmost position is the lorry with bread, the lorry next to it has rice.


(Updated ordered set)
Destination Genoa Hamburg Nantes

Origin French Polish Lithuanian
Colour blue red black green
Ferry Time 5 o'clock 6 o'clock 8 o'clock
Load coffee rice bread

(Updated unordered set)
Destination
Origin British Spanish
Colour
Ferry Time 9 o'clock 7 o'clock

Load

So Marseille can be the destination for either of the lorries at the right end, as potatoes can only be in the middle lorry or the leftmost one (5). Now only the colour of the fourth lorry is unknown, and I know that there is a white lorry next to a Spanish lorry (11). This makes the fourth lorry white, the fifth lorry is Spanish and coming in at 7 o'clock, while the fifth lorry is British coming in at 9 o'clock. Also, the Spanish lorry is somewhere to the right of the lorry headed for Marseille (9), which means the fourth lorry is going to Marseille, while the fifth is headed to Lisbon.


Destination    Genoa     Hamburg    Nantes      Marseille   Lisbon
Origin French Polish Lithuanian British Spanish
Colour blue red black white green
Ferry Time 5 o'clock 6 o'clock 8 o'clock 9 o'clock 7 o'clock
Load coffee rice bread

With that the solution is complete, with no more data available to firmly establish which lorry carries potatoes, so either the blue or black one could be carrying tea, the other commodity we haven't been given any information about.



This may not be the most efficient way to explain (or even solve), but this is the best way I can explain what I did to reach the solution.


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