Posted by Kaushik on Tuesday, February 26, 2008 at 8:59pm.
Break 120 up into a product of prime numbers. Then break that list into as many combinations of three numbers as you can think of, using all of the numbers. Examples:
120 = 1*2*2*2*3*5
= 1*(2*2*2)*(3*5)= 1x8x15
= 2*(2*2)*(3*5)= 2x4x15
= 1*2*(2*2*3*5)=1x2x60
= (2*2)(2*3)*5= 4x6x5
= 2*(2*5)*(2*3)=2x10x6
etc
4x + 10 -3x =2-3
120 = 2*2*2*3*5
So we need triples of these that multiply to get 120, but we must not forget that 1 can also be used.
So I went about it sort of systematically
1,1,120 ----- only case with 2 ones
1,2,60
1,3,40
1,4,30
1,5,24
1,6,20
1,8,15
1,10,12 --- to got more would repeat some
2,2,30
2,3,20
2,4,15
2,5,12
2,6,10
4,3,10
4,5,6
8,3,5
Done, 16 of them