The contiguous 4x4 restriction is impossible. If you have a valid 4x4 block, and shift it right one column, the four entries in the new column must match (as a group) the four entries in the departed column. This implies any 1x4 vertical box has the same entries as the box 4 cells to the right, although possibly rearranged. abcdw efghx --> {a,e,i,m} = {w,x,y,z} ijkly mnopz q...v Now consider shifting the 1x4 boxes down one row. They must still be equal as sets, so the operation of bringing in one new element into each set, and deleting the old ones, must preserve the set equality. {e,i,m,q} = {x,y,z,v} This is only possible if either the two removed elements are equal (a=w) and the two added elements are equal (q=v), or, in each set separately, the element added equals the element removed (a=q and w=v). But these possibilities are forbidden by the sudoku row and column no-repeat rule. This suggests a new kind of combinatorial object, keeping the contiguous box rule, but dropping the row & column restrictions. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of Kerry Mitchell Sent: Sat 4/14/2007 4:14 PM To: math-fun Subject: [math-fun] hexadoku grids Hi, I'm looking for solved hexadoku grids (like sudoku, but 16x16 instead of 9x9). Ideally, I'd like to find symmetric grids or grids where each contiguous 4x4 block uses each character only once, not just the main 4x4 blocks. Any hints? Thanks, Kerry Mitchell -- lkmitch@gmail.com www.fractalus.com/kerry _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun