# Puzzles

If you don't like solving puzzles, then you probably don't like maths much either, because the two are basically the same thing.

Puzzles come in all shapes and sizes and levels of difficulty and there are whole websites full of them. To see some of these, please go to the Websites page.

Here are a few puzzles aimed at different age groups and levels of difficulty. Try some of them out, and you will experience the thrill of finding that you can both understand more than you think you can, and that you are able to make connections using the understanding you currently have.

It is a good idea to look back over a successful puzzle solution and remind yourself how you did it.

Finally, don't be too quick to look at the hints and solutions. Give your self the time and space to find the solution yourself: it ismuch more fun that way.

## Here are some simple puzzles aimed at year 6, 7 & 8

1. Two farmers are taking their cows to market. On the way, one says to the other, "If you give me one of your cows, we would have the same number of cows." The other farmer replies, "True, but if you give me one of your cows, I will have twice as m any as you.". How many cows did the two farmers each have?

**Click here for a hint:**

**Click here for the solution:**

**Click here for the explanation:**

2. A boy has twice as much money as his friend. If they have 84p together, how much does each have?

**Click here for a hint:**

**Click here for the solution:**

**Click here for the explanation:**

3. Along a certain street the lights are placed 30m apart. If there are 10 lights, how far is it from the first to the last?

**Click here for a hint:**

**Click here for the solution:**

**Click here for the explanation:**

4. 2 ice-creams are eaten by 2 children in 2 minutes. How long will it take 5 children to eat 5 ice-creams?

**Click here for a hint:**

**Click here for the solution:**

**Click here for the explanation:**

5. An electric train is travelling due north. If the wind is blowing from the north west, in which direction is the smoke blowing?

**Click here for a hint:**

**Click here for the solution:**

**Click here for the explanation:**

Many thanks to David Feather (one of my lecturers at Bristol Poly back in the early 80s) for these and many other puzzles which I have been using since 1981.

## Here are a few geometric problems for years 9, 10 & 11.

These problems come from UK Maths Challenge papers.

6. A window frame in Salt's Mill, just outside Bradford in Yorkshire, consists of two equal semi-circles and a circle inside a large semi-circle with each touching the other three as shown. The width of the frame is 4m.

What is the radius of the circle in metres?

**Click here for a hint:**

**Click here for the solution:**

**Click here for the explanation:**

7. The diagram shows an annulus, which is the region between two circles with the same centre. Twelve equal touching semi-circles are placed inside the annulus. The diameters of the semi-circles lie along the diameters of the outer circle.

What fraction of the annulus is shaded?

**Click here for a hint:**

**Click here for the solution:**

**Click here for the explanation:**

...and finally, a really tough one!

8. Three squares are drawn on the outside of a right angled triangle, whose shorter sides have lengths *a* and 2*a*. The whole figure is surrounded by a rectangle, as shown.

What is the ratio of the area of the shaded region to the area of the outer rectangle?

**Click here for a hint:**

**Click here for the solution:**

**Click here for the explanation:**