# Squared Chain Puzzle

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Object: Fill the board with a chain of connected rods. Each rod has to be one unit shorter or longer than the previous rod.

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Contributed by: Karl Scherer (October 2015)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Click the board on any of the 8x8 positions. Click the board at any of the 8x8 squares. Now click the board on an empty position to the north, south, east, or west of the previous click to display a new green rod and a new link.

There must be only free positions between the current and the last clicked position.

After your click the board the system automatically connects it with the new link. There is a special condition, however:

There is a special condition: the connection between the last and the new link must be one unit longer or one unit shorter than the previous connection. For example, a rod of length 3 must be followed by a rod of length 2 or 4.

You win if you have covered the whole board with a continuous chain. You lose if you run out of moves. Some challenges have black squares that you cannot click.

Some challenges have no-go zones (black squares). You can always amend a board setup (see "setup" control below).

Expert level: Once you have covered the board, try to do so with the least number of moves. All solutions have been found by hand by the author. Can you find shorter solutions?

Best games known:

7x7 - 28 moves (using no diagonal moves) 8x8 - 32 moves (using no diagonal moves) 9x9 - 41 moves (using no diagonal moves) 10x10 - 47 moves (using no diagonal moves) 11x11 - 53 moves (using no diagonal moves) 12x12 - 60 moves (using no diagonal moves)

7x12 - 36 moves (using one diagonal move) 7x12-2 - 47 moves (using some diagonal moves) 7x7-2 - 48 moves (using some diagonal moves) 7x7-3 - 26 moves (using some diagonal moves) 7x7-4 - 30 moves (using some diagonal moves) 7x7-5 - 15 moves (using some diagonal moves)

8x8-2 - 32 moves (using some diagonal moves) 8x8-3 - 15 moves (using some diagonal moves) 8x8-4 - 30 moves (using some diagonal moves) 8x8-5 - 30 moves (using some diagonal moves) 9x9-2 - 46 moves (using some diagonal moves) 9x9-3 - 32 moves (using some diagonal moves) 9x9-4 - 42 moves (using some diagonal moves) 9x9-5 - 44 moves (using some diagonal moves)

Controls

The "challenge" pop-up menu and the "select" setter bar allow you to select a board. You can choose between five square boards and a few extra challenges.

"save" stores the current board position, "reset" recalls it.

"moves" displays the number of moves you have played.

The "take back move" button allows you to go back one move.

The "back to start" button takes you all the way back to the start.

"step length" shows you the length traveled in the last move.

Click "numbers" to display the sequence numbers of the links on the playing board.

"diagonal" toggles: if activated, diagonal moves are allowed.

"solution" all challenges now come with a solution.

"setup" toggle: if activated, you can amend the board. Click an empty board position to create a wall; click a wall to delete it.

History

The "Squared Chain Puzzle" was first published by the same author as the Zillions game "Squared Chain" in 2015. The Zillions game did not come with the diagonal moves option, though.

## Permanent Citation

"Squared Chain Puzzle"

http://demonstrations.wolfram.com/SquaredChainPuzzle/

Wolfram Demonstrations Project

Published: October 26 2015