"Alpha math" problems, where each letter stands for one digit of a number, can help you identify some of the things you know about the behaviors of particular base ten digits under various operations. Your task is to decode each of the following problems, figuring out what digit each letter represents. Note 1
In the following sums, one letter always represents the same digit in each problem, and no digit is represented by more than one letter. Replace the letters with digits:
Consider the following:
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What does the sum of a and a in the hundreds column tell you about the value of a?
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Notice that the sum of b and c in the tens column is different from the sum of c and b in the ones column. What does this tell you about the value of b + c?
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Notice that the sum of b and c in the tens column is b. What does this tell you about c?
Each letter represents a different digit of a number:
Decode the problem to determine the following value:
Problem A3
In these problems, the asterisks represent missing digits (though they do not all represent the same digit, as do the letters in the previous problems). Identify the missing digits in the following multiplication problems:
Problem A4
Each letter represents a different digit of a three-digit number. Decode the problem:
Jen has found a special five-digit number that she calls abcde. If you enter the number 1 and then her number on a calculator and multiply it by 3, the result is the same number with a 1 on the other end:
