The five-digit number 6☐432 is divisible by 11. What digit goes in the box?

Explanation

1. 01

   Digits in odd places (1st, 3rd, 5th): $6 + 4 + 2 = 12$. Digits in even places: $\square + 3$.

2. 02

   The difference $12 - (\square + 3) = 9 - \square$ must be 0 or a multiple of 11.

3. 03

   So $\square = 9$, giving $69{,}432 = 11 \times 6{,}312$.