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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 as that of another tile. A player is able to play one of their tiles alongside another tile if both pairs of numbers on the sides of the touching tiles match. See diagram for example. 1) If the tile consisting of three 5's is played at the beginning of the game, find how many tiles can be validly placed next to it in the following turn. 2) If a tile consisting of 1,2,3 read clockwise around the tile is played at the beginning of the game, how many tiles can be validly placed next to it on the following turn?

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 as that of another tile. A player is able to play one of their tiles alongside another tile if both pairs of numbers on the sides of the touching tiles match. See diagram for example. 1) If the tile consisting of three 5's is played at the beginning of the game, find how many tiles can be validly placed next to it in the following turn. 2) If a tile consisting of 1,2,3 read clockwise around the tile is played at the beginning of the game, how many tiles can be validly placed next to it on the following turn?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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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 as that of another tile. A player is able to play one of their tiles alongside another tile if both pairs of numbers on the sides of the touching tiles match. See diagram for example. 1) If the tile consisting of three 5's is played at the beginning of the game, find how many tiles can be validly placed next to it in the following turn. 2) If a tile consisting of 1,2,3 read clockwise around the tile is played at the beginning of the game, how many tiles can be validly placed next to it on the following turn?
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 as that of another tile. A player is able to play one of their tiles alongside another tile if both pairs of numbers on the sides of the touching tiles match. See diagram for example. 1) If the tile consisting of three 5's is played at the beginning of the game, find how many tiles can be validly placed next to it in the following turn. 2) If a tile consisting of 1,2,3 read clockwise around the tile is played at the beginning of the game, how many tiles can be validly placed next to it on the following turn?
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