Arrange shapes by cutting or folding

Question

The castle gardener has a square for each type of rose. There are three roses in her garden. The queen has requested a new rose to be planted. If the gardener moves just three garden planks one time only, she can get four squares. How can this be accomplished

square 1

square 2 square 3

Answer 1

Often, it is easier to think of a problem in reverse of how it is written. It is also often a good idea to draw it out if you do not see the answer right away. Think of it this way:

What is the lowest number of equal length planks it would take to make 4 squares with side lengths equal to the plank lengths?

Answer: 12

What is the highest number of equal length planks it would take to make 3 squares with side lengths equal to the plank lengths?

Answer: Again 12

If you were allowed to move four planks, could you convert the four square figure into three squares?

Pause here to think about it

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If you were allowed to move four planks, you could move the 4 blue planks and end up with the following 3 squares.

However, you can only move 3 planks, so one of those 4 planks needs to remain stationary.

Can you think of a way to do that?

Pause here to think about it

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Since you were only allowed to move 3 planks, you could do it with the following moves:

Now, just reverse the moves to go from three squares to four squares:

Answer 2

Difficult to make a picture.

From the square on the left take the top plank and place it to the right of the top plank on the top square.

From the square on the left take the left plank and place it below the plank you just placed completing a square.

From the square on the left take the bottom plank and slide it to the right completing a square.