Chapter 1

 Million Mystery The "million mystery" number is 9,687,534. 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.