No Primes Here

     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 b instead of digits.

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