Did you solve it? The broken vase

Ceramic Conservator Penny Bendall works on one of three monumental Chinese Porcelain Vases at the Fitzwilliam Museum in Cambridge, Wednesday March 29 2006. T Photograph: Chris Radburn/PA

Earlier today I set the following three puzzles:

1. With two straight line cuts, divide the vase into three pieces that can be reassembled to form a square.

Note: we’re working in 2 dimensions. You need to cut this shape into three pieces that can be reassembled with no overlaps or gaps. Photograph: alex bellos

2. Which single word can be placed in each of the eight marked spaces to make eight meaningful sentences?

_ I kicked him in the leg yesterday.

I _ kicked him in the leg yesterday.

I kicked _ him in the leg yesterday.

I kicked him _ in the leg yesterday.

I kicked him in _ the leg yesterday.

I kicked him in the _ leg yesterday.

I kicked him in the leg _ yesterday.

I kicked him in the leg yesterday _.

3. The three directors of a bank are deeply suspicious of one another, and agree a system of locks and keys for the bank’s safe, such that:

• No single director can open the safe alone.

• Any two directors can open the safe by pooling their keys.

What is the smallest number of locks and keys they need to open the safe, and how do they distribute them?

Solutions

1. One straight line cut will give you two pieces, each with a single straight side. Since the desired shape, a square, has four straight sides of equal length, you need to figure where to make these two cuts of equal length. The cuts need to also be at right angles, which limits the options…

2. The word is ‘only’.

Only I kicked him in the leg yesterday, I only kicked him in the leg yesterday, I kicked only him in the leg yesterday, etc.

3. The directors need to put three locks on the safe, and they need two keys for each lock, making a total of six keys.

If the locks are A, B and C, then the keys need to be distributed as follows: A and B to one director, B and C to another, and A and C to the third. In this way, no single director can open the safe, but any combination of two directors can.

I hope you enjoyed today’s teasers. They are extracted from my latest puzzle book So You Think You’ve Got Problems which is out in paperback in the UK on Thursday. You can preorder it here at The Guardian Bookstore.

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.