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There are four buses; their origins are the cities of A, B, C, and D. their destinations are the cities of E, F, G, and H.

They park in a gasoline station in a line to get fuel. after a while, they start to go to their destinations (not in the order of cities they are from and/or going to, which was mentioned in the first paragraph).

Information (in the gas station):

  • the bus that is destined to E is exactly in front of the bus that is originated from A.
  • the buses that are destined to F and G, are placed consecutively in the line (the order of these two buses is unknown).
  • one of the buses is going from B to H.
  • the origin of the first and last buses in the line is one of the cities B and C.

Question: If the last bus is destined to F, then which city is the origin of the bus that is going to E?

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The origin is D

Logic:

The last bus is going to F, and G is next to F, so the 3rd bus is going to G

This means the first two buses are going to E and H in some order.

B is going to H and has to be either first or last, so it's first (B -> H).

This means Bus 2 is going to H. All destinations determined.

C must be last, so bus 2 and 3 are A or D in some order.

A is behind the bus going to E, which is 2, so A must be in slot 3.

Order:

B -> H

D-> E

A -> G

C -> F

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  • $\begingroup$ I believe you made a typo in the line where you wrote where bus 2 is headed $\endgroup$ – Danny Harding Aug 10 at 2:37
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Some quick logic:

- From the second point and the fact that the bus destined to F is in last place we know that the order is (Front to back) ?, ?, G, F
- The last two points and the point above means the bus from B to H is in first (as it cant be last, as thats going to ), and therefore the bus from C is last. The order is now H, E, G, F and the origins are B, ?, ?, C
- The first points means the origins must be B, D, A, C

So the final orders are

H, E, G, F and B, D, A, C

And therefore the origin of the bus going to E is

D

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Actually

the condition that the buses that are destined to F and G, are placed consecutively in the line is redundant (the question can be answered without it)

because

We know that the buses #1 and #4 go from B and C, and the bus #4 goes to F. But the bus from B is going to H (not F), so it must be the bus #1. So, the bus #4 must go from C (to F). Since the bus to E is not going from A (we know that these buses are different), that bus must arrive from D, the only remaining city. Question answered.

Additionally

we can determine all the bus routes (without using the condition mentioned above) and their order. The D-E bus must be #2 (since it's not #1, which is B-H, and it stands in front of A-somewhere, which is not #4). So, the remaining bus #3 goes from A to the only remaining location: G. Final answer: #1 B-H, #2 D-E, #3 A-G, #4 C-F.

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