From The Sunday Times, 26th February 1961 [link]
“We’re a biggish family in more ways than one”, said Jeremy. “Five, including triplets, and three of us the same height. I’m 6 ft. and aged 72; Jim is three inches taller than John and three years older; and John and Julian’s combined heights are 5 ft. 11 in. more than Joe’s and their combined ages 71 years more than his. Our aggregate height in inches equals our aggregate age in years, but no one’s age in years equals Joe’s height in inches”.
What were the name, age and height of the tallest of the triplets?
This was the first of the regular Teaser puzzles published in The Sunday Times. It was accompanied by the following introduction:
Brain-Teasers: a Weekly Feature
Great numbers of our readers have found entertainment and interest in the Brain-Teasers, or mathematical problems, which we have published from time to time, usually at holiday week-ends. Now we intend to make them a weekly feature of The Sunday Times.
Readers themselves have supplied many of the best of the problems in the past, and we invite them to continue to do so. A fee of £10 will be paid for each problem accepted.
Problems should fulfil the following conditions: Both the problem and the solution must be expressible in reasonably brief compass. No advanced or specialist mathematical techniques should be necessary. Solutions should be unique, or otherwise admit of no uncertainty in judging. Problems must be original. Diagrams are admissible if they are not too complicated.
The problem below is the invention of a reader who observes: “Any who are stumped by it after the expiry of an hour should feel cause for concern”.
A prize of £3 was offered.
[teaser1]
Frits and 
GeoffR are discussing. 
Dilwyn Jones, and 1 other are discussing. 
S2T2 
Jim Randell 6:01 pm on 27 July 2020 Permalink |
This Python program uses the [[
Football()]] helper class from the enigma.py library. It runs in 84ms.Run: [ @replit ]
from enigma import (Football, irange, update) # scoring system football = Football(points=dict(w=3, d=1)) # available digits digits = set(irange(0, 6)) # the columns of the table (table, gf, ga) = (dict(w="??T??", d="?TE??", l="AIA??", points="?SR?S"), "?MS?I", "?EE??") # allocate match outcomes for (ms, d) in football.substituted_table(table, vs=digits): # 7 of the (10) games have been played if not (sum(m != 'x' for m in ms.values()) == 7): continue # choose a value for M for M in digits.difference(d.values()): d_ = update(d, [('M', M)]) # allocate scorelines for ss in football.substituted_table_goals(gf, ga, ms, d=d_, teams=[1, 2]): # over half (4 or more) of the matches were 1-1 if not (sum(s == (1, 1) for s in ss.values()) > 3): continue # output solution football.output_matches(ms, ss, teams="CFRTU", d=d_)Solution: The results in the 7 played matches are: C vs F = 1-1; C vs R = 1-1; F vs R = 0-1; F vs T = 4-0; F vs U = 0-1; R vs T = 1-1; R vs U = 1-1.
The C vs T, C vs U, T vs U matches are yet to be played.
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Frits 2:01 pm on 29 July 2020 Permalink |
I tried to solve the problem with a SubstitutedExpression.
I succeeded but had to solve all major logic myself.
I wonder if in MiniZinc core van be achieved.
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