Partition Bingo

In attempting to solve a problem on a puzzle site that asked for 3 consecutive integers whose digit sums divided their digit products, I traveled down the rabbit hole of number theory and may have a new sequence to submit to the Online Encyclopedia of Integer Sequences (OEIS), and a name for these types of numbers (psi numbers, for product/sum=integer). As part of the process of investigating these numbers with some AI agents, it turns out that partitions of integers, which are just different ways to add up to the integer in question, can be used to construct psi numbers from their digit sums. To practice this construction, you can play something close to bingo, and this game allows you to enter a digit sum, give its prime factorization, and then examine all the partitions to see if they can divide their digit products. Instructions are in the game, but if you want more info on psi numbers, you'll have to wait for the psi number app on my website. Coming soon!

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