Brain-Teaser 510: [Angling competition]
From The Sunday Times, 21st March 1971 [link]
Announcing that the Baron’s team had won the angling competition, the Mayor told those assembled that the winning catch weighed 19st 1lb 7oz and consisted of plaice, halibut and turbot. He also disclosed the remarkable fact that each fish of the same kind had been precisely the same weight — each plaice 2lb 8oz, each halibut 4lb 1oz and each turbot 6lb 6oz.
Although His Worship mentioned that half the total number of fish in the winning catch were of one and the same kind and that there were three times as many of one kind as of one other kind, he lamentably failed to give the further details so many were waiting to hear.
One enthusiast, for example, wished to know the total weight of all the plaice landed by the Baron’s team.
Can you say what it was? (Answers in lbs).
This puzzle was originally published with no title.
[teaser510]
S2T2 
Jim Randell 9:40 am on 21 November 2019 Permalink |
Using oz for for measuring weight, we have:
So the total weight of fish is:
And the individual types of fish weigh:
This Python program uses the [[
express()]] function from the enigma.py library. It runs in 110ms.from enigma import (express, div, printf) # find numbers of plaice, halibut, turbot for s in express(4279, (40, 65, 102), min_q=1): t = sum(s) # half the total was of one kind h = div(t, 2) if h is None or h not in s: continue # and there were 3 times as many of one kind than of an other if not any(3 * x in s for x in s): continue # output solution (p, h, t) = s printf("plaice = {p}, halibut = {h}, turbot = {t}")Solution: The total weight of plaice was 82 lb, 8 oz (= 82.5 lb).
There were 33 plaice (= 1320 oz = 82 lb, 8 oz = 5 st, 12 lb, 8 oz).
There were 11 halibut (= 715 oz = 44 lb, 11 oz = 3 st, 2 lb, 11 oz).
There were 22 turbot (= 2244 oz = 140 lb, 4 oz = 10 st, 4 oz).
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