4x4 #6

Solid puzzle.  Drop a comment in with the base used for each answer for those who struggled.  You’ve got a knack for the pure math puzzles!

Thanks for the solve! And yes, good idea - I’ll write it up.

Here’s the list of the bases used for each clue:

* 1A: base 6; 1001 - 234 = 323; (217 - 94 = 123)
* 4A: base 4; 1101 / (1 + 1 + 0 + 1) = 123; (81 / 3 = 27)
* 5A: base 2; 10 + 10 = 100; (2 + 2 = 4)
* 1D: base 5; 14 x 14 = 331; (9 x 9 = 81)
* 2D: base 3; 11! = 220; (4! = 24)
* 3D: base 8; (3 + 3)^3 = 323; (3 + 3)^3 = 216

In general, a helpful strategy is to list out the possible entries for each clue in several bases to see what lines up. Some additional helpful pointers:

* 5A must be either 020 or 100, so that gives you one digit right away
* The factorial clue must be a small base, since the number of digits in a factorial increases rapidly. This is enough in conjunction with 5A to solve both clues.
* The value of 3D is known since it’s only single digits in the clue (decimal 216); it must be at least base 7, or else it has too many digits
* Similarly, 4A is guaranteed to be divisible by 3, which helps to narrow down the base
* 1D is actually quite constraining; once 5A is solved, it should confirm this base as well

Thanks everyone for solving! This was fun to make and I hope to do more like this sometime!

https://youtu.be/7OEF3JD-jYo?si=HIbT0WMYTSFrTIGR

Numbers #3 - Base-ics

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