# Bogglers

By Scott Kim|Sunday, July 1, 2001

Child's Play

In a world of PlayStations and Nintendo, old-fashioned paper-and-pencil games still have charms

Ship Shapes

One hot afternoon, Alfie and Betty decide to play games indoors, in air-conditioned comfort. They start with Battleship. Alfie secretly places his fleet of five ships on a 5x5 grid. Two of the ships are three squares long, and there is one ship each of two, four, and five squares long. Ships may not overlap and may not be placed diagonally. Betty "bombs" one square of the grid at a time by specifying x,y coordinates to figure out where Alfie has placed his ships.

Alfie marks each bombed square with an explosion when a bomb hits a ship or with a drop of water if a bomb misses. When all squares of a ship have been bombed, it sinks. There are six hits and two misses in the arrangement shown at right. Note that one of the three-square-long ships has been sunk.

In the following three battleship games, all the bombs are misses. Can you deduce where all five ships must be?

 1 2 3

In the following three games, each bomb hits a different ship. Can you figure out where all five ships must be?

 4 5 6

Trick-tac-toe

1. The children move on to the game of tic-tac-toe. Alfie draws an X in the upper left corner box of a standard 3x3 board. In which of the remaining eight boxes should Betty draw an O if she doesn't want to lose?

2. The children tire of three-in-a-row tic-tac-toe, so they decide to see who can be the first to get three adjacent marks in an L pattern. Betty makes the first move in a corner, as Alfie did in game 1. In which of the remaining eight boxes should Alfie draw an O if he doesn't want to lose? If they continue the game, both playing as well as possible, who wins?

3. Now Alfie and Betty try playing on a 4x4 board. As in regular tic-tac-toe, three in a row wins. What should the first player's strategy be?

4. This 4x4 game is still too easy for these clever kids. Alfie and Betty play again but with a twist: The first person to get three in a row loses. After several close wins, they finally end a game in a draw. No one gets three in a row, but the board is full of X's and O's. Can you draw this final board? There are four possible answers.

Blocked In

For their last contest of the afternoon, Alfie and Betty play dots and boxes on a 5x5 grid. Best out of three games wins the tournament. In dots and boxes, two players take turns drawing lines to fill in the sides of a box. When a player completes a box by drawing in the fourth side, the player initials that box and must draw another line. When all 25 boxes have been completed, the player with the most boxes wins.

 Game 1: Alfie has four boxes, while Betty has three (see below). It's Betty's move. Assuming both players always complete a box whenever they can, who will win, and what will the final score be? Game 2: It's Alfie's move in this as-yet-scoreless game. He thinks he's going to lose but then has a brilliant insight that will allow him to win this game. Where does Alfie make his next move? Game 3: It's the tiebreaker; the winner takes the tournament. So far, Alfie is behind six boxes to one, and it's Betty's move. How can Alfie win? Hint: Use the trick from the previous game.

Solution

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Got new solutions for the puzzle? Want to see other people's solutions? Talk to the puzzle master in his discussion forum at www.scottkim.com.

For more puzzles and inventions by Scott Kim, see his Web site, www.Scottkim.com, or his book Inversions: A Catalog of Calligraphic Cartwheels, Key Curriculum Press, 1996.