PUZZLE
AND GAME PAGE
Rotation Puzzles: There are three rotation puzzle devices that can be accessed by using the link below that connect you to the website of John Pais. Puzzles for this device are taken from the unit Permutation Puzzles and are also given in the file Rotating Puzzles, in case you want to obtain a printout. The [3,3] device on John's website has a puzzle indicator that you can toggle to obtain 3 of these puzzles. The other devices do not currently indicate any puzzles. The inversion puzzles for these devices are given in the Rotating Puzzles file. Some of the patterns that can be imagined cannot be obtained by the rotations that the devices allow. This includes at least one of the puzzles in that file. You are encourage to make up additional puzzles for any of these devices.
The [3,3]-puzzle device is at http://kinetigram.com/CG/CycleGadget/CycleGadget1B.html
The [3,4]-puzzle device is at http://kinetigram.com/CG/CycleGadget/CycleGadget2B.html
The [3,4]-puzzle device is at http://kinetigram.com/CG/CycleGadget/CycleGadget3B.html
[3,3] Rotating Puzzle Device: This device has 2 chambers with 3 disks in each. Either chamber can rotate moving the disks in the chamber along with the shared disk. A clockwise rotation of the left chamber followed by clockwise rotation of the right one has this result. Warning: Some patterns that can be imagined for this device cannot be obtained by these rotations.
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The Inversion Puzzle: If possible, start with the disk in the initial positions on the left and obtain the pattern on the right. |
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The Diagonal Puzzle: If possible, start with the disk in the initial positions on the left and obtain the pattern on the right. |
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The Top Switch Puzzle: If possible, start with the disk in the initial positions on the left and obtain the pattern on the right. |
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The Up-Down Puzzle: If possible, start with the disk in the initial positions on the left and obtain the pattern on the right. |
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Other Rotating Devices: The [3,3] rotating puzzle devices is a special case of a [k,j] puzzle device.
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[3,4] Inversion Puzzle: If possible, start with the initial pattern on the left and obtain the one on the right. |
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[3,4] Up-Down Puzzle: Start with the initial pattern on the left and obtain the one on the right. |
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[3,5] Inversion Puzzle: If
possible, start with the initial pattern on the left and obtain the one on
the right. The permutation for this puzzle is |
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You are encouraged to can make up additional puzzles.
The Thinkadot Puzzle: Think-a-Dot consists of a box with eight windows thru which colored dots can be seen. There are holes on top, labeled as f or g or h. A marble can be dropped into any hole. There are also exit holes on each side, allowing the marble to exit. The dots are attached to pivots that are hidden from view. As the marble falls, it strikes a pivot. The pivot directs the marble left or right, depending upon the pivot’s orientation. Then, the pivot reverses orientation, simultaneously displaying the other color. Blue dots direct the marble left, pink dots direct the marble right.
Don Love, a faculty member at
http://www.webster.edu/~lovedo/thinkadot/think_a_dot.html
John Pais has a different ladybug version of this device, which you can run directly from his website.
kinetigram.com/CG/LBGateGroups/LBGateGroups.html.
Aside from differences in graphics, his version asks you to make a pattern and then try to change it back to an initial setting.
A strategy for solving these puzzles can be found by selecting Thinkadot Strategy. Our unit Thinkadot Algebra gives a partial analysis relating this puzzle to remainder concepts. Our unit Thinkadot Group gives an advance analysis relating this puzzle to the decomposition of finite abelian groups.
Magical Attribute Square Puzzles: In a magical attribute square each row and each column has a shape of each type and a color of each type. A magical attribute square is a magic attribute square if the two diagonals also have this property. Arrange these attribute items into a magic attribute square. You can use the MS Word version with Ctrl x to cut and Ctrl v to paste. There is also a Token Template file if you want to make tokens these attribute items. This file also has a template for making tokens for other types of attribute items and for making numerical tokens.
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Any solution to this puzzle can be used to make a magic number square. Assign a different number from {0,1,2,3} to each color. Assign a different number from {0,1,2,3} to each shape. Multiply the fist number by 4 and add the second number. This assigns a number from {0,1,¼ ,15} to each attribute item. Replace each attribute item by this number.
For more ideas about magical
squares see
Finding 3by3 Magical Squares and Constructivist Learning Resources
Attribute Game The basic game uses the basic set of attribute items below on a Venn diagram board with hidden label. Two teams compete to see which of them can find the names of the label with the fewest number of wrong trials in placing items in various regions. More advanced games use more attribute items.
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Other
Types of puzzles will be added later.