So I was thinking about sudoku and realized that I'm not fond of the asymmetry of the 3 kinds of groups of 9 boxes that must each contain all the digits. Just rows & columns would be fine, but the 9 3x3 squares of boxes don't seem to fit in well. So I wondered if something could be done with a 4-dimensional tic-tac-toe board T -- with #(T) = 3^4, like sudoku. The most obvious groups of 9 cubes seem to be the "coordinate 2-planes": Just specify 2 of the 4 coordinates of points in T, letting the other two range over their 9 combinations; there are 54 such 2-planes in T. To make this as sudokitudinous as possible, the only problem remaining is to choose -- in a symmetrical fashion -- 27 among these 54 2-planes. ***It's tricky to find a symmetrical way to choose 27 out of the 54 2-planes!*** The best ways to do this all seem unsatisfactory, in that they don't have S_4 or even A_4 symmetry w.r.t. the coordinates x1, x2, x3, x4. Ideas? --Dan