A certain right triangle has all integer lengths. One of the triangle’s legs is 24 inches. What is the sum of all possible lengths of the other leg?

*Solution to yesterday’s problem:*

Let’s use our favorite method to solve this problem: the blanks method. There will be 10 blanks for 10 digits:

____ ____ ____ ____ ____ ____ ____ ____ ____ ____

The first digit can be any number. The second digit can be any number *except* the one used in the first digit, and the same principle goes for the third digit.

__10__ __9__ __8__ ____ ____ ____ ____ ____ ____ ____

The fourth and fifth digits can be any number from 0-9.

__10__ __9__ __8__ __10__ __10__ ____ ____ ____ ____ ____

The last five digits, however, can only be one digit: the digit used in its corresponding spot of the palindrome. For instance, the last digit must be the same as the first digit.

__10__ __9__ __8__ __10__ __10__ __1__ __1__ __1__ __1__ __1__

We don’t need to divide by anything because in phone numbers, order matters! Multiplying the numbers together, we find that there are *72,000* phone numbers that fit the bill.

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