Transforming Tetrominoes

A tetromino is a shape made by putting four equal-sized squares together so that each square shares at least one side with another square. Neither flipping over nor turning changes the shape of a tetromino. Tetrominoes come in five shapes, called I, L, O, T and Z after the capital letters they most closely resemble. Which two tetrominoes cannot be converted into one another by re-positioning just one of the four squares?

O and Z I and O T and Z L and Z

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1 solution

Robert Singleton
Mar 21, 2018

The solution is: I and O. If you remove any square from the "O" tetromino, which is a 2 x 2 square, the remaining part is called an L-tromino. By reattaching the square in a different place, you can form a T, an L, or a Z, but because of the bend, you cannot form the I. The I is the only tetromino that does not contain the L-tromino.

Note: "I and Z" is not one of the given answers. If it had been given, it would also qualify as a solution. If you remove one square from the end of the I, you cannot form a Z by attaching it to the remaining three squares in a row. Similarly, if you remove one square from either end of the Z, you cannot form an I by attaching it to the remaining L-tromino.

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