**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.

[enigma526]

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As originally published the puzzle has many solutions. The inclusion of the word “any” makes this a viable puzzle and is probably what the setter had in mind.

This recursive Python program runs in 103ms.

Run:[ @repl.it ]Solution:There are 161 sheep, and 168 cows on the farm.So the total number of animals is 329.

The distribution of animals in the fields is:

I found this solution would not run under the Geocode solver, but did run OK under the Chuffed solver.

Keeping the number of cows the same in the four fields, I got the same single solution as Jim

I noticed that the digit 7 seems to be the key to this enigma, since:

1) All the totals of (sheep, cows,total) are divisible by 7 for each of the four fields

2) The possible transfers of sheep between fields are divisible by 7

3) The total sheep(161), cows(168) and total animals(329) are all are divisible by 7

I also found that by varying the number of cows in the four fields, this gave multiple solutions,

so the number of cows in each field must be the same to give a single solution.