1300.11 – Mystery Number

The number has five digits. Two of them are zeros. The sum of all five digits is twenty. The digit in the thousands’ place is not zero, and it is three times the value of the digit in the tens’ place. The number is at least 10,000. What is the number?

Solution

This takes a bit of trial and error. First, assign each digit a letter. We’ll call the number $abcde$ .

From the given information, we know that $b = 3 d$ , and, since $b \neq 0$ , it follows that $d \neq 0$ . Additionally, since we know that $abcde \geq 10000$ , it follows that $a \neq 0$ . We now know that $c$ and $e$ must be the zeros. Hence, our number takes the form $ab0d0$ , and $a+b+d = 20$ .

After some trial and error, we arrive at the solution: 89,030.