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Seven Puzzles for G4G7*


by Serhiy Grabarchuk

The Gathering for Gardner (G4G) is the unique biennial event founded in 1993 by Gardner fan and puzzle collector, Tom Rodgers. Many enthusiastic and talented folks are organizing it in Atlanta every second year, and the World's foremost mathematicians, puzzlers and magicians, deeply influenced by Martin Gardner's work and life, are attending G4G's. 

Gathering in Atlanta, each G4G participant brings with him/her some writings related to math, magic, or puzzling, and prepared specially to honor Martin Gardner. Then these pieces are exchanged between all G4G participants. The seven different puzzles below are my Exchange Gift for G4G7.

Printable Pieces    

Printable Puzzle: To solve some of the puzzles which will be described below you can print their pieces/grids. For this, click the respective image marked with the "pp" pictogram (as that shown at left) to go to a new window with the puzzle pieces/grids; then you can print them and (when necessary) cut them out. Note that all these puzzles are copyrighted, so you can print them for your own use only, and not for any kind of commercial profit.

Play Puzzle    

Play Puzzle: Click an image marked with the pictogram shown at left to go to a page with an interactive version of the respective puzzle.
Puzzle I
Squaring the Seven
Divide the Seven shown below into five parts and rearrange them into a square as that shown in the illustration. The grids within the Seven and square are provided just for the purpose of showing the exact proportions of its elements, so you can use the grids’ lines as you will wish, but the Seven’s area has to be fully used. Pieces can be rotated and turned over, but not overlapped.
Click this image to go to the Printable Puzzle page.Printable Pieces
Divide the Seven into five parts so that to rearrange them into a square..
Puzzle II
Seven Stars
With three straight lines divide the Seven shown below into seven parts so that each part contains a single star. Find two substantially different solutions.
Click this image to go to the Printable Puzzle page.Printable Pieces
Divide the Seven into seven parts with a single star each.
Puzzle III
The Coin Seven Challenge
The Seven shown below at left is assembled of six coins. Light and dark circles represent different sides of coins. Moving one coin at a time, exchange coins in the Seven exactly as shown below, in the right diagram. Could you achieve this in five single moves? Important. To ensure an exact position for each coin after its move, it must touch to at least two coins from the unmoved group. But remember that there is one illegal move when you simply move a coin between two other ones so that all the three coins form a straight line.

In five single moves invert the Seven's pattern.
Puzzle IV
Halving the Match Seven
Using two matchsticks, divide the Seven shown in the illustration below into two parts of the same area. The lines within the Seven are provided just to show its exact proportions. Note that matchsticks in the puzzle are used as math segments of length 1, and each matchstick must be used with all its length, so no loose ends of matchsticks should be formed. Matchsticks must not overlap each other, and you are not allowed to break and/or bend them.
Click this image to go to the Printable Puzzle page.Printable Pieces
With two matchsticks divide the Match Seven into two parts of the same area.
Puzzle V
The Seven Fish Seven
Using all the seven fish shown in the illustration below, form the Seven presented just next to them. Pieces can be rotated, but not overlapped and/or overturned.
Click this image to go to the Printable Puzzle page.  Printable Pieces
Using all the seven fish, form the Seven shape.
Puzzle VI
The Origami Seven
You have a square piece of paper colored on one of its sides and white on the other; it is a so-called Origami square. The challenge is to fold it exactly seven times so that to get a smaller, flat square with the Seven within it exactly as presented below in the right diagram.

You are allowed to fold one or several layers of paper at a time, counting this as a single fold; such a simple fold is called a “book fold." Thus, the final square may have several layers of paper in any of its points. Each plain color element of the square may be either a really plain color surface, or consist of several one-colored parts. It is true about each white part as well.

The dotted lines on the Seven are provided just for the purpose of showing its exact proportions; it is obvious that the Seven is inscribed within a 3x3 grid. Note that the back side of the final square may have any pattern. Also, bear in mind that the shown mutual sizes of the starting Origami square and the final square with the Seven are relative.

You can mark and pre-crease all necessary lines to folds using some additional tools, but before you start to fold the Origami square and counting folds, it must be fully unfolded and flat.

In exactly seven simple folds get the Origami Seven.
Puzzle VII
Eight Knights in the Seven
Eight chess knights -- four white and four black ones represented by small circles -- are placed on the 7-like chessboard as shown in the left diagram below.

Now, performing just normal knight’s moves from cell to cell of the chessboard, exchange the white and black knights as shown in the right diagram below.

Can you exchange the knights in exactly twelve moves, counting a consecutive series of leaps of a knight as one move? Hint. To achieve this goal you should perform moves by knights of different colors alternately.

To solve the puzzle you can use eight small coins placed directly on a big board; to get to it, click any of the challenge diagrams just below.
Click this image to go to the Printable Puzzle page.Printable Pieces
Exchange the white and black knights in exactly twelve knight's moves.
Also, you can go to our page with the interactive Flash version of the puzzle. You can also click the image just beneath.
Click this image to go to the interactive version of the puzzle.Play Puzzle
Play our interactive Flash version of the puzzle.


Puzzle Solutions
Notes & References
*) This seven-puzzle collection was developed specially for the Gift Exchange at the Seventh Gathering for Gardner (G4G7), Atlanta, Georgia, USA, March 16-19, 2006. It is published in the G4G7 Exchange Book, published by Gathering 4 Gardner, Inc. in 2007.
Many new puzzles of the types described in this article can be found in my book,
The New Puzzle Classics: Ingenious Twists on Timeless Favorites, published by Sterling Publishing Co., Inc. in 2005:
     -- Chapter 1: Puzzling Dissections, pages 16-41;
     -- Chapter 3: Matchsticks & Coins, pages 72-97;
     -- Chapter 4: Witty Patterns, pages 98-126;
     -- Chapter 6: Origami Puzzles, pages 154-181;
     -- Chapter 7: Tricky Moves, pages 182-209.
     Also, nice collections of dissection, matchstick, coin, put-together and moving piece puzzles are gathered at
Puzzles.COM in its Puzzle Playground section.
Last Updated: July 3, 2011
Posted: May 28, 2006
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