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Let the number N be the smallest three digit number with digits $a,b,c$. $a+b+c+ab+bc+ca +abc=29$. Evaluate $\frac{N+1}{5}$.

By adding $1$ on both sides we get $(a+1)(b+1)(c+1)=30$. How should I proceed further and is there any way without hit and trial?

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1 Answer 1

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We want to find the smallest $N$ possible, so minimise each digit one at a time.

$a \ne 0$ so the smallest $a$ is $1$. This gives $(b+1)(c+1) = 15$ and you can continue from here.

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