Some Special Three-Digit Numbers

Number Theory Level 5

How many \(3\) digit numbers \(N\) are there such that the digits of \(N\) and \(3N\) are all even?

Details and assumptions

All of the digits of \(N\) and \(3N\) are even. For example, \(N=200\), \(3N=600\) will be a valid solution. However, \(N=600\), \(3N=1800\) will not be valid, due to the '1' in \(1800\).

There is not restriction on the number of digits of \(3N\).


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