A number theory problem by A Former Brilliant Member
Number Theory
Level
2
A man owns a mini-zoo that contains dogs, cats, tigers and fishes. There are 12 heads and 36 legs in that zoo (excluding the head and the legs of the man). How many fishes are there if there are 4 dogs and 3 cats?
The answer is 3.
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1 solution
We actually don't need to be told the number of dogs and/or cats.
36 = 4d + 4c + 4t + 0f
12 = d + c + t + f
First equation minus 4 times second equation: -4f = -12
f = 3