#math trivia for #September16: #259 has two squares side by side. Do any day-numbers have two squares overlapping?

— Burt Kaliski Jr. (@modulomathy) September 17, 2013

The side-by-side squares are of course 25 and 9. The problem doesn’t state exactly how much overlapping is allowed, so many forms are possible. Presumably, every digit is involved in at least one of the two squares. At least one digit must be involved in only one square, otherwise the solution is trivial (i.e., every square would overlap itself).

- abc where these portions are squares
- a and abc: 100, 121, 144, 169, 196
- ab and abc: 169, 256, 361
- ab and bc: none
- abc and b: 144, 196
- abc and bc: 100
- abc and c: 100, 121, 144, 169, 289, 324, 361

- bc where these portions are squares:
- b and bc: 16, 49
- bc and c: 49, 64, 81