TileWhirlStar tray challenges
These puzzles work on both star trays: 45 tiles (3 × 3 points) and 80 tiles (4 × 4 points).
Five tiles meet at the center and all touch each other. No tile stays put when you turn the tray, so every tile moves in a group of five.
Three-Tone
MediumFill the tray so no two tiles sharing an edge are the same color. Use as few colors as you can.
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Two colors seem like they should work, but the five center tiles form a ring of five, and a ring of five cannot alternate. Three is the answer: on the 45-tile tray it comes out at exactly 15 of each.
Five Corners
HardNo two tiles that touch may share a color, not even tiles that meet at a single point.
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The five center tiles all touch each other, so five colors is the minimum. Five is also enough, with 9 tiles of each color (16 each on the 80-tile tray).
Spin Five
MediumBuild any design that looks the same after a fifth of a turn.
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Every tile belongs to a group of five that must match, so every color count must be a multiple of five. You are really choosing just 9 tiles (16 on the 80-tile tray) and repeating them.
Mirror Match
EasyBuild half the star, then build the other half as its mirror image.
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Each mirror line runs through one point and out through the opposite notch. Only the tiles on that point's diagonal sit on the line.
Kaleidoscope
HardMake a design that looks the same when turned and when mirrored.
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Design one half of one point (6 tiles, or 10 on the 80-tile tray) and the rest is decided. Over half the patterns in the library are kaleidoscopes, so you can check your thinking against them.
Odd Point Out
Easy to mediumAlternate two colors around the five points.
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You can't: five is odd, so the run always breaks somewhere. The puzzle is deciding where to put the break. Broken Symmetry in the pattern library is one answer.
Tile Budget
MediumRebuild any pattern using only three colors, or no more than 10 tiles of any one color.
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Open-ended. Look for colors that can stand in for each other.
Half Star
MediumThe pentagon in the middle of the star is exactly half the tray by area. Color it one way and the five points the other.
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The pentagon's edge cuts straight through some tiles. On the 45-tile tray, 15 tiles sit inside it and 15 more are cut in half. Any consistent rule for the cut tiles gives a different, valid star.
Memory Flash
EasyStudy a pattern page for 30 seconds, cover it, and rebuild it from memory.
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Score one point per tile in the right place, out of 45 or 80.
Fewest Swaps
MediumBuild one library design and turn it into another by swapping two tiles at a time, in as few swaps as you can.
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Pick two designs with the same tile counts.
Five Points (2 players)
All agesTake turns placing a tile of your own color anywhere. When the tray is full, each point belongs to whoever has more tiles in it. Most points wins.
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On the 45-tile tray the game can never end in a draw. Use white and black, the only two colors with enough tiles, and swap who starts each game.