Can you solve it? The broken vase

Broken Chinese Vase
Photograph: Juzant/Getty Images

My puzzle book So You Think You’ve Got Problems is out in paperback this week. Here are three problems from it. The first is about a vase, the second is about a leg, and third is about a set of keys.

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?

I’ll be back with the answers at 5pm UK.

Meanwhile, NO SPOILERS!

UPDATE: You can now read the solutions here.

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.

So You Think You’ve Got Problems is a book of puzzles and word games for all abilities. The paperback is out on Thursday, but you can preorder it here at The Guardian Bookstore.