Tricycle is a 2-D permutational puzzle, somewhat similar to Rubic's cube. It has 37 particles with three different colors. The purpose of the game is to rotate the circles left or right so the particles with the same colors occupy the same sector of the circle.
- Mouse: move the mouse pointer close to the center of the given circle and click to rotate left or right.
- Keyboard: Use W, A, D keys to set the focus on a given circle and then ← or → to rotate the selected circle.
- Tap close to the center of the given circle to rotate left or right.
The game uses the following notation to identify the moves:
- T / t: rotate the top circle right or left.
- L / l: rotate the left circle right or left.
- R / r: rotate the right circle right or left.
If you are stuck, you can use Hint or Solve buttons to help you out. Hint uses a recursive search to find the next best move, Solve uses a genetic algorithm to find the solution.
The following calculation needs to be reviewed and demonstrated.
The puzzle has 37 pieces: 37! = 13,763,753,091,226,345,046,315,979,581,580,902,400,000,000
- 12 red "eyes": 12! = 479,001,600
- 7 green "eyes": 7! = 5,040
- 5 blue "eyes": 5! = 120
- 6 red "stars": 6! = 720
- 4 green "stars": 4! = 24
- 3 blue "stars": 3! = 6
The total number of possible permutations: 37! / (12!*6!*7!*4!*5!*3!) = 458,240,149,608,416,150,976,000
Rubik's cube possible permutations = 43,252,003,274,489,856,000
Does this mean, that Tricycle has 10,000 more permutations than Rubik's cube? Wow!
We have 6 possible movements (top circle, left circle, right circle) * (rotate left, rotate right)
6^30 < 37! / (12!*6!*7!*4!*5!*3!) ==> does this mean, that 30 movements are not enough to solve the puzzle from any shuffled state?
6^31 > 37! / (12!*6!*7!*4!*5!*3!) ==> is it possible to solve with maximum 31 permutations from any shuffled state?