Question

Take any three-digit number and arbitrarily rearrange its digits. Prove that the difference between the original number and the new number is divisible by `3`. Is this also true for four-digit numbers?

Difficulty level (1 very easy - 10 very hard): 3

Topics:
Number Theory -> Modular Arithmetic / Remainder Arithmetic -> Divisibility Rules -> Divisibility Rules by 3 and 9
Sources:
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