Teaser 2482: [Running up that hill]
From The Sunday Times, 18th April 2010 [link]
Jan went up the hill and down, and up and down again, running each stretch at a steady speed and taking a whole number of minutes for each of the four stretches (rather more going up!). John timed her over the first two-thirds of the overall course, Mark timed her for the middle two-thirds, and Philip over the final two-thirds. All three times were the same whole number of minutes. The time taken on one stretch was a two-figure number of minutes whose two digits, when reversed, gave the time taken overall for all four.
What, in order, were the times taken on each of the four stretches?
This puzzle was originally published with no title.
[teaser2482]
S2T2 
Jim Randell 11:06 am on 30 September 2025 Permalink |
If we suppose the times taken on each of the 4 sections are A, B, C, D.
The for the timings to be the same whole number value, we have:
From which we see that each of A, B, C, D (and hence the total time T = A + B + C + D) must be multiples of 3.
This Python program runs in 75ms. (Internal runtime is 5.8ms).
from enigma import (irange, decompose, all_same, nrev, printf) # decompose T/3 into C/3, B/3, C/3, D/3 for (b, d, a, c) in decompose(irange(4, 32), 4, increasing=1, sep=0): (A, B, C, D) = (3*a, 3*b, 3*c, 3*d) # check times are the same if not all_same(A + B + 2*c, a + B + C + d, 2*b + C + D): continue # calculate total time T = A + B + C + D X = nrev(T) if not (X > 10 and X in {A, B, C, D}): continue printf("A={A} B={B} C={C} D={D} -> T={T}")Solution: The times taken were: A = 21 min; B = 9 min; C = 27 min; D = 15 min.
And the total time is 72 min.
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