Take any 3 digit multiple of 37, If you rotate the digits, you still get multiples of 37.

For example, use 518, which is 14 x 37. If you rotate the digits you get 185 which is 5 x 37. Rotate them again and you get 851 which is 23 x 37.

Another example is 629, which is 17 x 37. If you rotate the digits, you get 296, which is 8 x 37. Rotate them again, and you get 962 which is 26 x 37.

This works with any 3 digit multiple of 37, including the ones that are 3 digits because we have 0 as a leading digit.

It does NOT work if you change the order of the digits in a non-rotation. For example, going back to the 518, if I change the order of the digits in a non-rotation to 158, this is NOT a multiple of 37.

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