Teaser 2849: Swift tailor
From The Sunday Times, 30th April 2017 [link] [link]
When measuring gentlemen’s chest sizes in inches, the tailors five foot long tape overlapped so that the set of numbers 1 to 9 was aligned with a consecutive set of higher numbers.
Taking each pair of these nine aligned lower and higher numbers as a fraction the tailor saw that just two of the nine “fractions” were in their simplest form and did not cancel down (i.e. the pair of numbers had no common factor greater than one).
All of this was also true when he measured the smaller waist size.
What (in inches) were the gentleman’s chest and waist sizes?
[teaser2849]
Hugh+Casement and 
S2T2 
Jim Randell 10:00 am on 21 December 2021 Permalink |
Assuming the tape measure is graduated 1″ … 60″.
The smallest possible measurement is: 1/10 … 9/18 corresponding to a measurement of 9″ (although that is ludicrously small). And the largest is: 1/52 … 9/60 (corresponding to 51″).
This Python program runs in 46ms.
Run: [ @replit ]
from enigma import (irange, is_coprime, printf) # consider possible measurements for m in irange(9, 51): # count how many pairs are co-prime pairs = ((i, m + i) for i in irange(1, 9)) ps = list(p for p in pairs if is_coprime(*p)) # we are looking for measurements with 2 co-prime pairs if len(ps) == 2: printf("m={m} {ps}")Solution: The measurements are: chest = 42″; waist = 30″.
When the measurement is 30″ we get the following lowest term fractions: 1/31, 7/37.
When the measurement is 42″ we get the following lowest term fractions: 1/43, 5/47.
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Hugh+Casement 1:12 pm on 21 December 2021 Permalink |
That works out at 76 and 107 cm: a fine figure of a man!
Somehow I find 84 and 90 cm more realistic.
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