Given three different digits, it is easy to form all 6 possible 3-place numbers with them. Depending on the specific digits chosen, some of those numbers might be prime numbers, whereas others are composite. Take this case: 2, 3, and 5. 523 is prime, but 235, 253, 325, 352, and 532 are composite.

(It is even possible that all could be composite, but that’s another story.)

A similar situation occurs even if you have a pair of like digits and one other digit. An example might be 2, 3 and 3. 233 is prime whereas 323 and 332 are composites.

But consider the case of two pairs of similar digits. For example, a pair of 2’s and a pair of 3’s. What can be said about all possible 4-place numbers?

**Extra:** Generalize this by using ** a, a, b,** and

**instead of digits.**

*b*