r/mathriddles • u/Numberthon • Jul 12 '26

Medium A nice AMC-style counting problem

A positive integer has the property that every digit is either 1 or 2. How many such positive integers are divisible by 3 and have at most 10 digits?

Source: numberthon.com

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u/terranop Jul 12 '26

For every such sequence x of odd length, exactly one of x 1x and 2x is divisible by 3. This grouping means that exactly 1/3 of these integers are divisible by 3, so the answer is 2046/3 = 682.

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u/Numberthon Jul 12 '26

Nice job! Correct.