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Scoring with Dice

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Clement from Sha Tin College in Hong Kong has sent in this solution for Scoring with Dice:

For the first question, I had to find a combination using 4 numbers, and its product had to be 4 times its sum. I first tried to find a suitable number, with many factors. And it had to be big enough in order to fit the sum of the combination in.

I thought: 40 would probably be too small to fit the sum of the combination in and 44 only had 4 factors, so I tried 48. I listed all the factors: 2*24, 3*16, 4*12 and 6*8 and tried splitting each one of them into 4 steps, such as: 2*6*4*1 or 3*4*2*2 and I eventually came up with one: 6*2*2*2, the sum being 12.

I used the same method for the next two questions and came up with 5*3*2*2 which made 60, the sum being 12 and 3*3*2*2*2 which made 72, the sum being 12.

Thank you for this clearly explained answer Clement.