Enigma 375: Miles out
16 December 2016
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From New Scientist #1524, 4th September 1986 [link]
A French friend had a road journey to make from London and he knew the shortest distance in miles, so he wanted to know what fraction to multiply by to make it into kilometres.
“Just multiply by 2.”
“No, 3/2 is better.”
“No, 5/3 is more accurate.”
“No, 8/5 is more usual.”
Those were the suggestions made to him and each would have led him to calculate the distance as a whole number of kilometres.
The suggested fractions were, by chance, all obtained by taking a pair of successive terms in the well-known sequence 1, 2, 3, 5, 8, … where new terms are calculated by adding the two previous terms. This led me, knowing that one mile is 1.60934 kilometres, to calculate which pair of successive terms of the sequence would give the best fraction to use. I reported my findings to my French friend and this fraction, too, led him to calculate his distance as a whole number of kilometres.
How far, in miles, was his journey?