Enigma 1352: Old MacDonald
28 January 2014
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From New Scientist #2511, 6th August 2005
Older puzzlers know that 14 pounds make a stone and 8 stone make a hundredweight. Old MacDonald sold four varieties of potato, Primes, Queens, Roosters and Superb in 1-stone bags. One kind of bag, Chippers, contained an integral number of pounds of each variety, in order of increasing weight from Primes to Superbs; the other, Boilers, contained an integral number of pounds of each variety in order of increasing weight from Suberb to Primes. The number of pounds of each variety in each bag were different.
He also sold 1-hundredweight sacks of Commercial, which consisted of bags of Boilers and Chippers mixed. It so happened that in Commercial, half the weight of Superb came from Boiler bags and half from Chippers, and the number of pounds of Queens equalled the number of pounds of Roosters.
How many pounds of Primes were in 1 hundredweight of Commercial?