November 2018 - Math Problem

A game played with coins has the following rules.  

1. Coins are set up in a ​triangle.  
2. Coins are moved until the triangle is upside down.  
3. The number of moves is recorded.  

For example, if a two-layer triangle is used, then only one move is required to flip the triangle.  

Tokens with different patterns making a two-layer triangle

 

A three-layer triangle would only require two moves.  

Tokens with different patterns making a three-layer triangle
 

How many moves would a triangle with 5 layers require?

Solution:

A 5 layer triangle requires 5 moves.

Letters displaying five layer triangle

Five layer triangle showing five moves

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