Anna thinks of an integer that is not a multiple of three, not a perfect square, and the sum of its digits is a prime number. What could the integer be?
Solution
Since 12 and 21 are multiples of 3 (12 = 4 3 and 21 = 7 3), the answer is not 12 or 21. 16 is a perfect square (16 = 4 4) so the answer is not 16. The sum of the digits of 26 is 8, which is not a prime number, so the answer is not 26. Since 14 is not a multiple of three, 14 is not a perfect square, and the sum of the digits of 14 is 1 + 4 = 5 which is prime, then the answer is 14.
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