I was playing with a solver to the full house type puzzles, and I wanted to see what was the minimum number of squares that had to be blackened in order to get a puzzle with a single solution, thinking this would be a challenge since there would be so many places to start. It looks like for square puzzles of dim 3x3 and greater, two squares blacked out will generate a puzzle that has only one solution. Here are the first single solution puzzles for each dimension 3 to 14, sorted by lowest numbered squares (squares numbered from left to right, top to bottom). Note that after dimension 8x8 a stable pattern has developed such that blackening square 0 and square dimension+2 will yield a single solution. Perhaps a more interesting puzzle would be one in which you had to make the most decisions after you hit a black square, wall or barrier. Kirk Bresniker 0 5: +---+---+---+ | X | ^ | F | +---+---+---+ | ^ | > | X | +---+---+---+ | < | < | S | +---+---+---+ 1 solution. 1 7: +---+---+---+---+ | S | X | ^ | F | +---+---+---+---+ | v | ^ | > | X | +---+---+---+---+ | v | < | < | ^ | +---+---+---+---+ | v | > | > | > | +---+---+---+---+ 1 solution. 0 8: +---+---+---+---+---+ | X | < | < | < | ^ | +---+---+---+---+---+ | S | v | F | X | ^ | +---+---+---+---+---+ | v | v | < | ^ | ^ | +---+---+---+---+---+ | v | v | > | > | ^ | +---+---+---+---+---+ | v | > | > | > | > | +---+---+---+---+---+ 1 solution. 0 3: +---+---+---+---+---+---+ | X | ^ | > | X | < | ^ | +---+---+---+---+---+---+ | S | ^ | v | F | v | ^ | +---+---+---+---+---+---+ | v | ^ | v | ^ | v | ^ | +---+---+---+---+---+---+ | v | ^ | v | > | v | ^ | +---+---+---+---+---+---+ | v | < | < | < | v | ^ | +---+---+---+---+---+---+ | v | > | > | > | > | > | +---+---+---+---+---+---+ 1 solution. 0 18: +---+---+---+---+---+---+---+ | X | < | < | < | < | < | ^ | +---+---+---+---+---+---+---+ | S | v | < | < | < | ^ | ^ | +---+---+---+---+---+---+---+ | v | v | v | F | X | ^ | ^ | +---+---+---+---+---+---+---+ | v | v | v | < | ^ | ^ | ^ | +---+---+---+---+---+---+---+ | v | v | v | > | > | ^ | ^ | +---+---+---+---+---+---+---+ | v | v | > | > | > | > | ^ | +---+---+---+---+---+---+---+ | v | > | > | > | > | > | > | +---+---+---+---+---+---+---+ 1 solution. 0 10: +---+---+---+---+---+---+---+---+ | X | ^ | > | > | > | > | > | > | +---+---+---+---+---+---+---+---+ | ^ | > | X | < | < | < | ^ | v | +---+---+---+---+---+---+---+---+ | < | < | ^ | v | < | ^ | ^ | v | +---+---+---+---+---+---+---+---+ | ^ | > | ^ | v | v | ^ | ^ | v | +---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | F | ^ | ^ | v | +---+---+---+---+---+---+---+---+ | ^ | v | S | v | > | > | ^ | v | +---+---+---+---+---+---+---+---+ | ^ | v | > | > | > | > | > | v | +---+---+---+---+---+---+---+---+ | < | < | < | < | < | < | < | v | +---+---+---+---+---+---+---+---+ 1 solution. 0 11: +---+---+---+---+---+---+---+---+---+ | X | ^ | > | > | > | > | > | > | > | +---+---+---+---+---+---+---+---+---+ | ^ | > | X | < | < | < | < | ^ | v | +---+---+---+---+---+---+---+---+---+ | < | < | ^ | v | < | < | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+ | ^ | > | ^ | v | v | F | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | > | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+ | ^ | v | S | v | > | > | > | ^ | v | +---+---+---+---+---+---+---+---+---+ | ^ | v | > | > | > | > | > | > | v | +---+---+---+---+---+---+---+---+---+ | < | < | < | < | < | < | < | < | v | +---+---+---+---+---+---+---+---+---+ 1 solution. 0 12: +---+---+---+---+---+---+---+---+---+---+ | X | ^ | > | > | > | > | > | > | > | > | +---+---+---+---+---+---+---+---+---+---+ | ^ | > | X | < | < | < | < | < | ^ | v | +---+---+---+---+---+---+---+---+---+---+ | < | < | ^ | v | < | < | < | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+ | ^ | > | ^ | v | v | < | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | F | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | > | > | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+ | ^ | v | S | v | > | > | > | > | ^ | v | +---+---+---+---+---+---+---+---+---+---+ | ^ | v | > | > | > | > | > | > | > | v | +---+---+---+---+---+---+---+---+---+---+ | < | < | < | < | < | < | < | < | < | v | +---+---+---+---+---+---+---+---+---+---+ 1 solution. 0 13: +---+---+---+---+---+---+---+---+---+---+---+ | X | ^ | > | > | > | > | > | > | > | > | > | +---+---+---+---+---+---+---+---+---+---+---+ | ^ | > | X | < | < | < | < | < | < | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+ | < | < | ^ | v | < | < | < | < | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+ | ^ | > | ^ | v | v | < | < | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | F | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | > | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | > | > | > | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | S | v | > | > | > | > | > | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | > | > | > | > | > | > | > | > | v | +---+---+---+---+---+---+---+---+---+---+---+ | < | < | < | < | < | < | < | < | < | < | v | +---+---+---+---+---+---+---+---+---+---+---+ 1 solution. 0 14: +---+---+---+---+---+---+---+---+---+---+---+---+ | X | ^ | > | > | > | > | > | > | > | > | > | > | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | > | X | < | < | < | < | < | < | < | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | < | < | ^ | v | < | < | < | < | < | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | > | ^ | v | v | < | < | < | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | < | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | v | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | F | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | > | > | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | > | > | > | > | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | S | v | > | > | > | > | > | > | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | > | > | > | > | > | > | > | > | > | v | +---+---+---+---+---+---+---+---+---+---+---+---+ | < | < | < | < | < | < | < | < | < | < | < | v | +---+---+---+---+---+---+---+---+---+---+---+---+ 1 solution. 0 15: +---+---+---+---+---+---+---+---+---+---+---+---+---+ | X | ^ | > | > | > | > | > | > | > | > | > | > | > | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | > | X | < | < | < | < | < | < | < | < | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | < | < | ^ | v | < | < | < | < | < | < | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | > | ^ | v | v | < | < | < | < | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | < | < | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | v | F | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | v | ^ | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | v | > | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | > | > | > | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | > | > | > | > | > | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | S | v | > | > | > | > | > | > | > | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | > | > | > | > | > | > | > | > | > | > | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ | < | < | < | < | < | < | < | < | < | < | < | < | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 solution. 0 16: +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | X | ^ | > | > | > | > | > | > | > | > | > | > | > | > | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | > | X | < | < | < | < | < | < | < | < | < | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | < | < | ^ | v | < | < | < | < | < | < | < | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | > | ^ | v | v | < | < | < | < | < | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | < | < | < | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | v | < | ^ | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | v | v | ^ | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | v | F | ^ | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | v | > | > | ^ | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | v | > | > | > | > | ^ | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | ^ | v | v | > | > | > | > | > | > | ^ | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | S | v | > | > | > | > | > | > | > | > | ^ | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | ^ | v | > | > | > | > | > | > | > | > | > | > | > | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ | < | < | < | < | < | < | < | < | < | < | < | < | < | v | +---+---+---+---+---+---+---+---+---+---+---+---+---+---+ 1 solution. ---------------------------------------------------------------- Dear Ed, Here are the paths that solve each puzzle. The starting square is labeled with a letter for the column and a number for the row; succeeding letters give directions and numbers count forced moves. C5; R, D, L, 2, U, 12 C4; U, L, U, 6, L, D, 12 C3; D, R, U, R, 7, R, 12 It's interesting to note that puzzle 2.2 of the Qualifier has the path E5, L, U, 14. While being shorter and having fewer total turns, it incorporates the largest chunk of forced turns of any of the puzzles. Hmm. Bryce Herdt ---------------------------------------------------------------- The last one is particularly elegant. I don't suppose you could coax a few more of these out of Erich? Cheers, Jason Dyer ---------------------------------------------------------------- I solved the first two of these. In #1, start at c3 (chess notation), go right, down, left, and when you reach b6, go up, finishing at b2. In #2, start at c5, go up, left, up, and when you reach e2, go left, then down, finishing at e4. Joe DeVincentis ----------------------------------------------------------------- 7x7 start at row 5 column 3 going R: R1D2L3U5R1U1R5D6L2U1R1U4L1D2L1U1L2D3 42 moves covering 43 squares out of 49 leaving 6 black 8x8 start at row 4 column 3 going U: U1L2U1R1U1R6D7L3U1L2D1L2U4R1D2R2U4R3D5L1U4L1D2 57 moves covering 58 squares out of 64 leaving 6 black 9x9 start at row 3 column 3 going D: D3R3U5R3D1L2D2R2D1L1D2R1D2L8U8R4D4L1U3L2D6R5U1L3 73 moves covering 74 squares out of 81 leaving 7 black I had a lot of fun doing these, thank you very much for the introduction. Are there any more of these puzzles, or have they been freshly invented? I did a google search, but you don't want to know how many puzzles are called "Full House" ... is there another name for this type of puzzle? I know that the puzzles I like heavily depend on both the intelligence and dedication of the puzzle-makers. I wish I could thank them directly, but in any case, keep up the good work puzzle-meisters! Thanks again, Mark Ingram