The magic nine

Four games on the magic board

The magic nine

• The board has nine holes in a square, three by three, joined by the three rows, the three columns and the two diagonals. Place the balls numbered 1 to 9, one in each hole, so that every row, every column and both diagonals add up to fifteen.
• A trick that solves it: write 1 to 9 in three slanting rows to make a diamond. The four numbers that stick out of the square then slide across into the empty holes on the opposite side.

The magic seven

• Use only the balls 1 to 7, and leave empty the two holes to the left and right of the centre. Five lines remain: the top row, the bottom row, the middle column and the two diagonals. Place the seven balls so that each of these lines adds up to twelve.

Magic tic-tac-toe

• A game for two. One player has the odd balls, 1, 3, 5, 7 and 9; the other has the even ones, 2, 4, 6 and 8. Odd has one ball more and begins.
• Take turns placing one of your balls in any empty hole. Whoever completes a line of three that adds up to fifteen wins — no matter whose balls are in it. A full board without a fifteen is a draw.

Do-guti

• A blocking game from India, played on the four corner holes and the centre. The lines are the left and right sides and the two diagonals, so the board is an hourglass lying on its side. (With all four sides joined, nobody could ever be blocked.)
• Each player has two balls, one player on the two top corners and the other on the two bottom corners; the centre starts empty. Take turns moving one of your balls along a line to the next hole, which must be empty. Nothing is captured. If you cannot move on your turn, you have lost.

In this version

• In do-guti you have the balls at the top and move first. The same position three times is a draw.
• In tic-tac-toe you choose under New game whether to play the odd balls and begin, or the even ones. The machine looks five moves ahead.
• «Hint» places one ball correctly in the magic nine and the magic seven, using a solution that fits the balls you have already placed.

New game