In my puzzle blog earlier today I set you three pi-flavoured puzzles.

1. Move one matchstick below to make the equation **approximately** correct

**Solution**

2. G**odd**frey and St**even** are **p****i**-ous ninth century monks. It is the summer of 888 AD, and they have agreed they will share the job of writing the town records every day. Goddfrey does every day that contains an ODD digit in the date. Steven does all other days. They begin

- 20.08.888 Steven
- 21.08.888 Goddfrey
- 22.08.888 Steven
- 23.08.888 Goddfrey
- 24.08.888 Steven
- 25.08.888 Goddfrey
- 26.08.888 Steven
- 27.08.888 Goddfrey
- 28.08.888 Steven

*When is the next day when Steven has to work?*

**Solution**

2.2.2000. (2 Feb 2000)

I looked like a fair deal between the monks, but Steven gets a sabbatical that lasts a more than a thousand years.

3. I bought a delicious pie the other day. It cost somewhere between £1.50 and £2.75 inclusive. I gave a 24 per cent tip, and the total price was still an exact number of pence. When I paid with a £5 note I received five coins in my change (the fewest I could have been given).

*How much did the pie cost? **And what has this question got to do with pi?*

**Solution**

A 24 per cent tip means that the money paid was the cost multiplied by 124/100.

We can simplify this fraction to 31/25.

In order for 31/25 multiplied by the cost to be an exact number of pence, the cost must be a multiple of 25p.

So, the possible costs are £1.50, £1.75, £2, £2.25, £2.50, £2.75, giving total money paid as £1.86, £2.17, £2.48, £2.79, £3.10, £3.41, and change from a fiver as:

- £3.14, fewest coins £2, £1, 10p, 2p, 2p (FIVE)
- £2.83, fewest coins £2, 50p, 20p, 10p, 2p, 1p (SIX)
- £2.52, fewest coins £2, 50p, 2p (THREE)
- £2.21, fewest coins £2, 20p, 1p (THREE)
- £1.90, fewest coins £1, 50p, 20p, 20p (FOUR)
- £1.59, fewest coins £1, 50p, 5p, 2p, 2p (FIVE)

So, the pie cost EITHER £1.50 or £2.75.

And what has this got to do with pi? The two possible amounts of change are £3.14, or £1.59. Pi, to five decimal places is 3.14159. WOWZA!!!!

*Thanks to Chris Smith for todays puzzles. You can check him out on* *Twitter*.

*I set a puzzle here every two weeks on a Monday.** **I’m always on the look-out for great puzzles. If you would like to suggest one, email me.*

*I’m the author of several books of popular maths, including the puzzle books Can You Solve My Problems? and Puzzle Ninja.*