After the recent post about How Many Possible 4×4 KenKen puzzles there are, Tetsuya Miyamoto, the creator of KenKen, gave us the following insight: (edited by Mr. L for clarity)
“Permutations of an order of number 1 to 4 can be calculated, but it is only
how many variations of placing numbers, no calculation involved.
So if they would like to know how many numbers of 4×4 puzzles, they can
limit to “addition only”, and try to create all the possible puzzles only
with one solution. (but again, they have to think of how they put freebie in
it! It will double the number of puzzles!). If they spend the time for it, it
may be possible to know the number of permutations we have for 4×4.
If we think of 9×9, with all four operations, it may be more complicated
than chess or Shogi. Like the “Four Color Theorem”, this may be someone’s lifetime study.“
After posing my original question, I realized that the question may not have been clear in its intent. I had meant to ask how many permutations of the 4 digits are possible in the 4×4 grid. This question will be the subject of a future post. Happy KenKen-ing!
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[...] people commented to the post, and I also received an email from Tetsuya Miyamoto, the creator of KenKen. The problem posed for my students is a classical permutation exercise, and to make it a little [...]