Sum one special
Three different integers have a sum of 1 and a product of 36 - what are they?
Age
11 to 14
Challenge level
Problem
Three different integers have a sum of 1 and a product of 36.
What are they?
Student Solutions
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