Enigma 526: Ewe to move
18 November 2019
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From New Scientist #1678, 19th August 1989 [link] [link]
Each of the four fields at Sunny Meadows Farm contains some sheep and some cows. On the gate of each field is hung a sign saying what fraction of the animals in that field are sheep. The signs are 1/2, 1/3, 2/3, 1/4.
Farmer Gillian explained that if she exchanged the signs on [any] two of the fields then, by simply moving some sheep from one of the two fields to the other, she could return to a situation where each sign again correctly indicated the fraction of the animals that were sheep in that field.
As I walked round I noticed that the total number of animals on the farm was between 300 and 350.
How many sheep, and how many cows, were on the farm?
I added the “any” in square brackets, as without it there are many solutions to the puzzle.