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This puzzle, often called the "Reverse the Triangle Puzzle," appearsregularly in puzzle books. Four rows consisting of 1 coin in row 1, 2 coins inrow 2, 3 coins in row 3, and 4 coins in row 4 form the shape of a triangle.What is the fewest number of coins you need to move to flip the triangle 180degrees so that it points in the opposite direction? In the case of 4 rows, itrequires moving just 3 coins. The general solution for any number of rows canbe calculated by dividing the number of coins by 3 and ignoring any remainder.A triangle of 4 rows has 10 coins, so 10/3 = 3.333 leads to 3 moves. However,this calculation is fairly nonintuitive as to why it works and requires aninelegant maneuver of periodically discarding a remainder. In this paper, wepresent a more intuitive formula that always calculates the answer directly andnever produces a decimal answer. Further, we explore inverting other shapes(e.g., rhombus) and find an interesting connection to the formula fortriangles.

Inverting the 10-Coin Triangle Puzzle and Other Shapes: A New General Solution