# CiSRA Puzzle Competition 2009 - Solutions

This is the archive of the 2009 Puzzle Competition. Please visit the current competition site for information about the latest Puzzle Competition.

## C.4 Higher Calling

At first glance, this looks like noughts and crosses (or tic-tac-toe) on steroids. While standard noughts and crosses is played on a square 3×3 board, a well-known three-dimensional variant uses a cubic 4×4×4 board. This puzzle is based on a four-dimensional variant, which is played on a 5×5×5×5 hypercube, represented as a set of twenty-five 5×5 square two-dimensional slices.

There are 77 Xs on the board and 76 Os; so O is the player to move next. In fact, O's move is forced - there is only a single space on the board O can play in which prevents X from winning next turn. The move is in slice (2, 2) (the centre slice), in the space (2, 0) (the top-middle space). If O moves anywhere else, X will move in this space next turn and get 5 in a row (from the top-left space in the bottom-left slice, to the top-right space in the top-right slice).

(We use the notation that slice (0, 0) is the top-left 5×5 square, and slice (4, 4) is the bottom-right square; similarly, space (0, 0) within any slice is the top-left space, and (4, 4) is the bottom left space. This is only so we can describe the solution. It doesn't matter which notation you use, the answer to the puzzle comes out the same.)

It's now X's turn, and this time X has a forced move to prevent O from winning in O's following turn. X's forced move is at slice (0, 0), space (4, 0). The series of forced moves continues:

PlayerMove
slicespace
O(2, 2)(2, 0)
X(0, 0)(4, 0)
O(2, 0)(4, 0)
X(2, 1)(4, 1)
O(3, 1)(4, 1)
X(3, 3)(4, 1)
O(2, 2)(4, 1)
X(4, 2)(4, 1)

At this point, there is nothing player O can do to stop X from winning next turn. Whether O plays at (4, 3) (4, 1) or at (3, 2) (3, 1), X will play in the other space to win the game.

The sequence of forced moves encodes a secret word in the positions of the slices. Each slice represents a letter as follows:

Beginning with (2, 2) M, the move sequence spells out the answer to the puzzle: MACHISMO.