On this page you will find problems that give you the opportunity to practise and develop your skills. Look at the chapters in Smart Thinking to learn the methods you need to use and then tackle the problems as they come up. I will try to put a fresh batch of problems onto the website each month, so check in routinely.

You will find examples of all of the five main categories of problems: verbal reasoning, abstract reasoning, numerical reasoning, inductive reasoning and decision analysis test. I will also include examples of other types, like insight problems, but I will put them up randomly to you give you a chance to practise your skills on a range of different types. If you want a fuller explanation of how the answer is reached, let me know.

1. The Engagement Party

Diana, Jessica,Virginia, Bryan, James and Tom are old friends, who have known each other since childhood. Recently, they all left university at the same time and got themselves jobs. Even though they are in full time employment they still see each other regularly. For some time it has been clear that each of them has paired off and formed a stable heterosexual relationship with another member of the group. Now they have decided to get engaged and to announce their engagements at the same time to the rest of their friends at a party.

From the following information decide what engagements were announced at the party.

Tom, who is older than James, is Diana’s brother.

Virginia is the oldest girl.

The total age of each couple is the same although no two of them are the same age.

Jessica and James are together as old as Bryan and Diana.

2. A woman has four pieces of chain. Each piece is made up of three links. She wants to join the pieces into a single closed loop of chain. To open a link costs 2 cents and to close a link costs 3 cents. She only has 15 cents. How does she do it?

This problem comes from J. Metcalfe & D. Wiebe, ‘Intuition in insight and non-insight problem solving’, Memory & Cognition, 15, (1987), pp. 288-294.

3. In the days before watches were invented, clocks were valuable possessions. A man living in a remote area had one that kept very good time. However, he woke up one day to find it had stopped, so he had no idea of the correct time. He decided to walk to the next valley to visit his friend, who also had a clock that kept good time. He chatted with his friend for a while and then made his way home. He didn’t know the exact length of the journey before he started. How did he manage to set his clock correctly when he got home?

4. The triangle below points to the top of the page. Show how you could move three circles to get the triangle to point to the bottom of the page.

5. There are ten bags, each containing ten gold coins, all of which look identical. In nine of the bags each coin is 16 ounces, but in one of the bags the coins are actually 17 ounces each. How is it possible, in a single weighing on an accurate weighing scale, to determine which bag contains the 17-ounce coins?