Problem number 21. In the six digit integer papaya, different letters stand for different digits and the same letter always represents the same digit. Also, y equals p plus p equals a plus a plus a. What is the value of p times a times p times a times y times a? So let's simplify the equation that we're given in the problem. We know that y is equal to 2p is equal to 3a, and since all of these are whole numbers, y has to be a multiple of 2, and it's also a multiple of 3. But we also know y is a digit, and digits can only be up to 9. So in this case, since y is a digit and it's a multiple of 2 and 3, the only possible value for y is 6. That's the only multiple of 2 and a multiple of 3, that's a single digit. Now since we know y equals 6, we can solve the equation and see that p is equal to 3 and a is equal to 2, since 2 times 3 equals 6 and 3 times 2 equals 6. Now we know all the variables, so we can just solve the equation at the end. 6 times 2 times 3 times 2 times 3 times 2 is equal to 432. So the answer is a, 432.

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