Brain-Teaser 665: … Steady …
From The Sunday Times, 7th April 1974 [link]
There were six starters for the special handicap event for the youngest class at the school sports. All started at the gun, and none fell by the wayside or was disqualified.
Dave started quicker than Ed and finished before Fred. Colin finished two seconds after he would have finished if he had finished two seconds before Ed. Bob and Dave started quicker than Colin, and Bob was faster than Ed.
Alf, who won third prize, finished two seconds after he would have finished if he had finished two seconds after Colin.
Who won second prize?
This puzzle was included in the book The Sunday Times Book of Brain-Teasers: Book 2 (1981, edited by Victor Bryant and Ronald Postill). The puzzle text above is taken from the book.
[teaser665]
S2T2 
Jim Randell 8:38 am on 24 November 2022 Permalink |
If the total times are A, B, C, D, E, F. Then we derive:
From which we get 2 chains (shortest to longest time):
However we are told that A was in 3rd place, but we see there are at least 3 competitors (B, C, E) who finished in a shorter time, which would imply the best A could have placed was 4th.
So, assuming positions are ranked according to time, either the puzzle is flawed, or the goal of the race is to achieve the longest time, not the shortest.
In this latter case the finishing positions (longest to shortest time) are:
Solution: Dave won second prize.
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