Again the second question is more challenging than the first, although both are difficult. The wording of the second question is confusing, so make sure you read it carefully. Good Luck!

- Joan looked at her watch as the car pulled in to pick her up. “Right on time” she told her husband as she opened the door. “I bet you speeded.” He shook his head and said “No, I just started at the right time. If I’d averaged 6mph faster I’d have been five minutes early, but at 5mph slower and I’d have been 6 minutes late.” How far had he driven?
- If Sam had driven for 20mins less than the time he would have driven if he had driven 20 miles less than he did drive but at two-thirds the speed at which he drove, he would have driven 10 miles less than he did. If he had driven for 20mins longer than the time he would have driven if he had driven 10 miles less than he did drive but at three-quarters the speed at which he drove, he would have driven 20 miles further than he did. Confused? How far did Sam drive?

- When Annie was asked how old she is, she replied “My present age is five times what it five years hence will be, less five times what it was five years ago.” How old is Annie?
- When Ted was twice as old as Sue, her brother Clive was twenty-two. When Sue was twice as old as Clive, Ted himself was twenty-five. Their ages total one-nought-three, so now what must their ages be?

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Whilst maths problems can be challenging, as a department we aim to show students that it is definitely not boring or pointless. In their 1998 book “Why do buses come in threes?”, Rob Eastaway and Jeremy Wyndham say that “maths doesn’t just answer questions. It also provides new insights and it stimulates curiosity. Gambling, travelling, dating, eating, even deciding whether or not to run when it’s raining, all involve elements of maths.” We aim to spark students’ interest by the regular use of UKMT maths challenges and the UKMT Olympiad mentoring sheets to promote some of the fun and interesting problems to which maths can be applied.

The aim of this blog is to share some of the interesting problems and brain-teasers that can be found online and in books for you to try.

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