A “PiWord” is a sort of crossword puzzle/magic square where you can find the across and down digits in the digits of Pi. Because Pi is transcendental, if you go out long enough you’ll be able to find any number you like, so you can obviously create a PiWord that is as large as you like and containing any numbers you like.
But if you constrain the number of digits of Pi you’re allowed to explore, it get’s a LOT harder. For example, here’s one that is entirely within the first 1000 digits of Pi:
The numbers along the right and left are the locations in Pi where each of these across or down 4-digit sequence is found (where the leading 3 is at location 1).
There are many non-trivial (i.e., not repeating the same sequence) 4×4 PiWords within the first 1000 digits.
If you go down to a 3×3 PiWord you can find 2 within the first 50 digits of Pi.
I’ll leave it as a challenge to the reader to find the other! (Hint: It uses some, but not all of the same 3-digit sequences as above.)
(Note: Of course, every PiWord solution has another using the same numbers just flipped across the main diagonal. That’s obviously cheating, and doesn’t count as a separate solution!)
Another interesting challenge is to write the program needed to find these. Finding 3×3 PiWords in the first handful of digits, like the challenge just above, can be (barely) done by inspection, but anything larger pretty much requires a computer! (I, of course, wrote a version to get the 4×4 above. I would share it with you…but where’s the fun in that!? 🙂 )