For what digit $d$ is the five-digit number $2345d$ a multiple of 9?
I know that a number is a multiple of 9 if and only if the sum of its digits is a multiple of 9. So, I need to find a value of $d$ such that $2 + 3 + 4 + 5 + d$ is a multiple of 9. The sum of the first four digits is 14, so I need to add $d$ to get a multiple of 9. The smallest multiple of 9 that is greater than 14 is 18, so I can try $d = 18 - 14 = 4$. If I plug in $d = 4$, I get $23454$, which is a multiple of 9. I can check this by dividing $23454$ by 9 and getting a whole number, 2606. 