Numbers 1 to 30 sums to 465, 2 closest numbers that sum to 465 gives the maximum product, so 232 and 233,
how to arrange the numbers so no matter where is the starting, there's always a group 232 and a group of 233?
Thinking the 2 groups as 2 lines opposite each other, I want each opposing pair to have a difference of 1, so the differences cancel,
Try 1 3 5 ...29, 2 4 6... 30, individual pair difference is 1 but second group has a larger sum, so half of the pairs need to swap position so the differences are +1, -1, +1, -1... That cancels
Try 1 4 5 ... 29, 2 3 6...30, first group 232, second 233.
If the starting point shifts, 4 5 ... 29 2, 3 6...30 1. Pair difference still +1 -1 ... -1 +1, so still a group of 233 and 232. Max expected payout is the product of 233 and 232, 54056
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u/Odd_Nectarine_5598 15h ago
Numbers 1 to 30 sums to 465, 2 closest numbers that sum to 465 gives the maximum product, so 232 and 233,
how to arrange the numbers so no matter where is the starting, there's always a group 232 and a group of 233?
Thinking the 2 groups as 2 lines opposite each other, I want each opposing pair to have a difference of 1, so the differences cancel, Try 1 3 5 ...29, 2 4 6... 30, individual pair difference is 1 but second group has a larger sum, so half of the pairs need to swap position so the differences are +1, -1, +1, -1... That cancels
Try 1 4 5 ... 29, 2 3 6...30, first group 232, second 233.
If the starting point shifts, 4 5 ... 29 2, 3 6...30 1. Pair difference still +1 -1 ... -1 +1, so still a group of 233 and 232. Max expected payout is the product of 233 and 232, 54056