by **frazer** » Tue Jul 26, 2005 9:09 am

I wondered about this a little. It seems to me that if you put a random digit on a square in the grid, then you are reducing the number of valid sudoku solutions by a factor of 9. The total number of solution grids is 6.67e21, which lies between 9^22 and 9^23. Consequently, if you place randomly 23 numbers on a blank grid, you should expect just under 1 solution. Placing further clues randomly makes it less and less likely that there are solutions. Conversely, placing fewer than 23 numbers makes it likely that there are several solutions. Indeed, relating to another thread, placing 17 numbers randomly, you could expect 400000 solutions, and placing 16 numbers, you could expect about 3500000 solutions. So, purely on these "information-theoretic" grounds, I'd suspect that 23 clues (about 28.4%) is the PTP.