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Answer: 6, -2 and -3


36 = 6$\times$6
     = 2$\times$2$\times$3$\times$3 (prime factors)
     = 2$\times$3$\times$6 or 1$\times$4$\times$9 or 1$\times$3$\times$12 or 1$\times$2$\times$18
(only ways to factorise 36 into 3 different numbers)

6 $-$ 2 $-$ 3 = 1 is the only way to make 1 by adding/subtracting from these triples



This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.