## Brainteaser 1505: Waste not …

**From The Sunday Times, 14th July 1991** [link]

The “tangram” is an ancient Chinese puzzle. It consists of seven pieces which can be formed into a square (as shown) and into many other artistic shapes.

The middle-sized triangle, the square and the parallelogram are all twice the area of the smaller triangles, and half the area of the larger ones. All the angles are 45, 90 or 135 degrees. And in my version the lengths of the shorter sides of the largest triangles are 7 cm.

I have a thin rectangular sheet of card 70 cm by 91 cm from which I wish to cut as many such sets of tangrams as possible with the minimum amount of wastage.

How many complete sets can I make?

The text of this puzzle is taken from the book *Brainteasers* (2002, edited by Victor Bryant), so may differ from the puzzle originally published in the newspaper.

[teaser1505]

## Jim Randell 7:03 am

on26 March 2019 Permalink |The Tangram square shown, has sides measuring 7√2 cm. Which gives it an area of 98 cm².

The 70 cm × 91 cm piece of card has an area of 6370 cm².

So there is potentially enough card to make 65 complete sets with no wastage.

However the square shown does will not fit into the length or width of the card an exact number of times.

My solution is cut the card into 7 cm × 7 cm squares. This divides the card into 10 × 13 = 130 squares.

We then rearrange the Tangram into two squares:

These squares also measure 7 cm × 7cm.

So, we then cut 65 of the squares using pattern A, and the remaining 65 sets using pattern B, giving us 65 complete Tangram sets.

Solution:We can make 65 sets, with no wastage.LikeLike