Enigma 1273: Unless
5 December 2014
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From New Scientist #2431, 24th January 2004
That great artist Pussicato has painted a picture containing antelope, bears, cats and dogs. For aesthetic reasons he kept the following conditions:
Writing “a” for the number of antelopes in the picture, “b” for the number of bears and so on;
a + 6d = 2b + c + 20 unless a + 6d = 2b + c + 17;
a + d = b + 2c + 2 unless a + d = b + 2c + 1;
3a + 5d = 3b + 5c + 11 unless 3a + 5d = 3b + 5c + 12;
3b + 5c = 2a + 2d + 1 unless 3b + 5c = 2a + 2d + 3;
the total number of animals is odd unless it is divisible by 5.
How many of each animal are there in the picture?