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Answer: 18
100 = 50$\times$2$\times$1$\times$1 not all different
= 10$\times$5$\times$2$\times$1 good! Sum = 18
Is there another way?
Factors of 100 not used: 4, 20, 25
100 = 4$\times$25$\times$1$\times$1 not all different
= 4$\times$5$\times$5$\times$1 not all different. Cannot use 4
= 25$\times$2$\times$2$\times$1 not all different. Cannot use 25
100 = 20$\times$5$\times$1$\times$1 not all different. Cannot use 20
Product 100
Age 11 to 14
ShortChallenge Level 
Answer: 18
100 = 50$\times$2$\times$1$\times$1 not all different
= 10$\times$5$\times$2$\times$1 good! Sum = 18
Is there another way?
Factors of 100 not used: 4, 20, 25
100 = 4$\times$25$\times$1$\times$1 not all different
= 4$\times$5$\times$5$\times$1 not all different. Cannot use 4
= 25$\times$2$\times$2$\times$1 not all different. Cannot use 25
100 = 20$\times$5$\times$1$\times$1 not all different. Cannot use 20
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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