Five ferrets took part in a race at a local fete. The following details are known about the race.
· Zippy finished either 1st or 3rd
· Flip finished faster than Musk
· The smallest difference in finishing times was between Flip and Lightning
· The largest difference in finishing times was between Lightning and Tornado
In what order did the ferrets finish in? You may like to work in pairs to solve this.
Possible solution:
Let's use the letters F, L, M, T, and Z to represent the ferrets, and let's denote their finishing times by numbers. Without loss of generality, we can assume that the race was run from fastest to slowest, so F finished first and Z finished fifth.
From the given information, we know that:
- Z can only be first or third, so F, L, M, and T must be second, fourth, fifth, and third (in some order).
- F finished first, so the smallest time difference must be between L and F (not between F and Z, which is larger).
- F was closer in time to L than to T, so the largest difference must be between T and Z.
Let's now combine these clues to narrow down the possibilities. Since L finished just before or just after F, it cannot be last or second to last. Likewise, T finished just after or just before Z, so it cannot be first or second. That leaves only two possibilities for the order:
F L M T Z (L finished just after F, T just before Z)
or
F T M L Z (L finished just before F, T just after Z)
Now we need to use the clue that Flip finished faster than Musk. From the two possible orders above, we can see that only the first one satisfies this condition, since F is already first and could not have been slower than M. Therefore, the order of finish was:
1st: F (Flip)
2nd: L (Lightning)
3rd: T (Tornado)
4th: M (Musk)
5th: Z (Zippy)
Note that this solution assumes that there were no ties in the finishing times, which may not be realistic in practice. However, it is a valid solution given the constraints of the problem.