Glue Square

Geometry Level 2

A kid collected the following wood cuttings of equal size. He wants to glue the pieces together to make a square.

At least how many of them are needed?


The answer is 4.

Venkatachalam J by Venkatachalam J , 43, India

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1 solution

Venkatachalam J
Jul 13, 2018

The kid can glue 4 wood cutting and make the smallest square. Each of the wood cuttings has 9 small squares. Therefore, the smallest perfect square which is multiple of 9 is 4×9= 36 which is equal to 6×6=36. Also, the above diagram shows the feasible of creating smallest square with minimum 4 wood cuttings.

9 Helpful 1 Interesting 0 Brilliant 0 Confused

More algebraically - the pieces have a longest side of 5 units and contain 9 units; therefore the smallest square possible must be at least 5x5 and must have an area divisible by 9 units. 5x5 = 25, but isn't divisible by 9; 6x6 is larger, and is divisible by 9, and as shown above, is possible to create.

Tina Sobo - 2 years, 10 months ago

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However, that algebraic reasoning is not sufficient to show 6 is the answer. Using 9 blocks I can create a T shape with longest side 5, but these will not form a square of side 6. In fact, it is impossible to form a perfect square using these T’s, thanks to their difficulty in reaching corners.

Jason Carrier - 2 years, 10 months ago

It is not mentioned in the problem itself that the square has to be fully filled (perfect). You only mention the perfect square in the solution. So it can have gaps, making it possible to glue a square with just 2 pieces.

Alex Belman - 2 years, 9 months ago

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