ALIEN MESSAGES
1. The missing number is 15. The rule is subtraction: Each number in the bottom row is the number above it minus the number to its left.

2. The missing number is 21. The rule uses a kind of subtraction that treats the digits of each number separately. The first digit of the new number in the bottom row is the difference between the first digit of the number above it and the first digit of the number to its left. Similarly, the second digit of the new number in the bottom row is the difference between the second digit of the number above it and the second digit of the number to its left. For the purposes of this puzzle, the difference between numbers is always positive: The difference between 6 and 7 and the difference between 7 and 6 are both 1.
To get the missing number, split 36 into 3 and 6, and 17 into 1 and 7. The difference between 3 and 1 is 2, and the difference between 6 and 7 is 1. So the answer is 2 followed by 1, or 21.
3. The missing number is 12. This message seems to follow the same rule as message 1, but subtraction fails on the last number: 21 – 13 = 8, not 7. The correct rule requires adding up the digits of two numbers. The missing number (12) is the sum of the digits in 21 and 36. Yoshigahara considers this fiendish puzzle to be one of his masterpieces.

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