Advent calendar 2021
8 December
The sum of three integers is 51. The product of the same three integers is 836. What is the product of largest integer and the second-largest integer?
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836=2×2×11×19, and so for the product to be correct the integers could be:
- 1, 1, and 836 (=2×2×11×19)
- 1, 2, and 418 (=2×11×19)
- 1, 11, and 76 (=2×2×19)
- 1, 19, and 44 (=2×2×11)
- 1, 4 (=2×2), and 209 (=11×19)
- 1, 22 (=2×11), and 38 (=2×19)
- 2, 2, and 209 (=11×19)
- 2, 11, and 38 (=2×19)
- 2, 19, and 22 (=2×11)
- 4 (=2×2), 11, and 19
The only one of these whose sum is 51 are 2, 11, and 38. Therefore the product of the largest and second-largest integers is 418
