ExplanationStart by considering integer a, which is the most constrained variable. It is a positive one-digit number (between 1 and 9, inclusive) and it has four factors. Prime numbers have exactly two factors:

themselves and one, so only look at non-prime one-digit positive integers. That’s a short enough list:

1 has just one factor

4 has three factors: 1, 2, and 4

6 has four factors: 1, 2, 3, and 6

8 has four factors: 1, 2, 4, and 8

9 has three factors: 1, 3, and 9

So the two possibilities for a are 6 and 8. Now apply the two constraints for b. It is 9 greater than a, and it has exactly four factors. Check the possibilities:

If a = 6, then b = 15, which has four factors: 1, 3, 5, and 15.

If a = 8, then b = 17, which is prime, so it has only has two factors: 1 and 17.

Only b = 15 works, so a must be 6.

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Sandy

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