February 17th, 2012


Psychic powers

Pick a number, any number. I am going to use my psychic powers to either predict something about your number, or force you to pick a number that agrees with my prediction.

Well, okay, not *any* number. A 4 digit number with different digits.

Now take the digits of your number and rearrange them into the largest and smallest possible four-digit numbers you can make.

And then subtract them.

Repeat the process until the process changes your new number into itself.

Your new number is
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Minimal Sudoku

While on the subject of math, it turns out that 17 is the minimum number of clues for a Sudoku puzzle to be uniquely solvable.

"The strategy we used to finally solve this problem is an obvious one — exhaustively
search through all possible solution grids, one by one, for a 16-clue puzzle."

While not a mathematically elegant way of attacking the problem, it looks like the search method they developed and used may have other benefits.

And don't hold out hope for an elegant solution:
"It is worth noting that there have been attempts to solve the minimum number of
clues problem using mathematics only, i.e., not using a computer. However, nobody has
made any serious progress. In fact, while it is very easy to see that a sudoku puzzle with
seven clues will always have multiple completions, because the two missing digits can be
interchanged in any solution, finding a theoretical reason why eight clues are not enough
for a unique solution already seems hard."

This is reminiscent of the case of the Four Colour Theorem, which was the first notable case of a mathematical proof by computer in 1976. I don't think any progress has been made on just using brain power to prove that either.