Bogglers

By Scott Kim|Monday, August 02, 2004

SPACE GAMES

Nob Yoshigahara, the prolific Japanese puzzle designer whose work is featured in this month’s Bogglers, died on June 19, 2004, in Japan after a long illness. We are pleased to be able to offer the following puzzles, adapted from Puzzles 101: A Puzzlemaster’s Challenge (A. K. Peters, 2003), as a tribute to this creative puzzlemaster.


ALIEN MESSAGES

1. [Easy] The Sagan Extraterrestrial Telescopic Instrument has intercepted a mysterious numerical message from an alien civilization in a distant star system. Can you identify the missing numeral? Hint: The alien messengers rely on addition and subtraction, not higher math.

2. [Tricky] A year later the aliens send this slightly different message. What is the missing number? Hint: Message 1 and message 2 follow a similar basic arithmetic pattern.

3. [Very tricky] Two years later the aliens send yet another variation of the message. Can you fill in the blank circle? Hint: Message 3 and message 1 appear deceptively similar but are based on very different arithmetic patterns.


LUNAR MODULES

Each coin shown above represents a spherical module of a fictional moon base dubbed Copernicus, circa 2060. The original base, configured like the letter H, comprises eight modules connected by air locks. Your mission is to change the station from its current shape to one of the other configurations shown above, adhering to the following strict rules. Only one module can be moved at a time and only to a position where it touches at least two other modules. If a module is moved to a position where it touches only two other modules, the adjacent modules cannot be on opposite sides, since there would then be nothing to stop the moving module from slipping right through them.

For example, the blue module at right can move to position A, where it would touch two other modules. It cannot move to position B, because it would touch only one other module, and it cannot move to position C, because it would touch only two other modules on opposite sides.

1. [Easy] Can you change the letter H into shape 1 in two moves?

2. [Challenging] Can you change the letter H into shape 2 in three moves?

3. [Difficult] Can you transform the letter H into shape 3 in five moves?

4. [Experts only] Change O back to H, following the same rules. This can be done in seven moves.


SOLAR PANELS

The diagram at right shows the main solar collector panels that will power Copernicus. To make lunar transport easier, each panel must be cut into four smaller pieces, all the same shape (though some pieces can be mirror images of each other).

1. [Easy] Here is one way to cut panel 1 into four identical shapes. Can you find two other solutions? You may cut only along the edges of squares.

2. [Challenging] Here is one way to cut panel 2 into four identical shapes. Can you find four other solutions? Cut only along the edges of squares.

3. [Difficult] Here is one way to cut panel 3 into four identical shapes. Can you find three other solutions? Two solutions involve cuts only along the  edges of squares; the third requires diagonal cuts.

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