# Million Mystery

## Solution

The “million mystery” number is 9,687,534.

## Explanation

• Since the number is greater than one million but less than ten million, it must have 7 digits.
• An even number must have 2, 4, 6, 8, or 0 in the ones place.
• The only possible digits are 3, 4, 5, 6, 7, 8, or 9. Therefore, the digit in the ones place can only be 4, 6, or 8.
• Guess and check to see the possible combinations of 12 for the ones period. The only combinations ending in an even number are 3 + 5 + 4 or 5 + 3 + 4.
• That means the sum of the two digits in the tens place and hundreds place is 8. Therefore, 8 is the digit in the ten thousands place.
• The number in the hundred thousands place must be even, since it's twice the digit in the tens place. The only remaining even digit is 6.
• That means the 3 must be in the tens place, and the 5 must be in the hundreds place.
• The digit in the millions place is 2 more than the digit in the thousands place. The two remaining digits are 9 and 7. Therefore, the 9 must be in the millions place, and the 7 must be in the thousands place.