A game is made up of triangular tiles that are equilateral with a number from the set {0,1,2,3,4,5} in each of the three corners on every tile. Each tile can include repeated numbers and none of the tiles have copies in the game. Note that a tile can be identical if rotated to have the same numbers. This tile, for example, will be in the board game. A) Find the maximum number of unique tiles that can be in this game. The game has all possible tiles except for those where all three numbers form a strictly decreasing sequence when read clockwise from the largest number on the tile. This tile, for example, will not be in the game. B) Find the number of tiles in this board game.
A game is made up of triangular tiles that are equilateral with a number from the set {0,1,2,3,4,5} in each of the three corners on every tile. Each tile can include repeated numbers and none of the tiles have copies in the game. Note that a tile can be identical if rotated to have the same numbers. This tile, for example, will be in the board game. A) Find the maximum number of unique tiles that can be in this game. The game has all possible tiles except for those where all three numbers form a strictly decreasing sequence when read clockwise from the largest number on the tile. This tile, for example, will not be in the game. B) Find the number of tiles in this board game.
Chapter9: Sequences, Probability And Counting Theory
Section9.5: Counting Principles
Problem 40SE: A family consisting of 2 parents and 3 children is to pose for a picture with 2 family members in...
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Transcribed Image Text:A game is made up of triangular tiles that are equilateral with a number from the set {0,1,2,3,4,5} in
each of the three corners on every tile.
Each tile can include repeated numbers and none of the tiles have copies in the game. Note that a tile
can be identical if rotated to have the same numbers.
This tile, for example, will be in the board game.
A) Find the maximum number of unique tiles that can be in this game.
The game has all possible tiles except for those where all three numbers form a strictly decreasing
sequence when read clockwise from the largest number on the tile.
This tile, for example, will not be in the game.
B) Find the number of tiles in this board game.
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