## Hard

If you follow my rule with 15, then you’ll surely get 74. The routine can then also be seen, with what number you wish – say a score! With a score you can get 71, but with five just 80 you’ll see. So perhaps you can figure for fun, what the answer with 30 will be.

Set by JAH Hunter in Fun with Figures, submitted by Robb Gosine, postgraduate student

## Very hard

You are standing at the centre of a circular field of radius R. The field has a low wire fence around it. Attached to the wire fence (and restricted to running around the perimeter) is a large, sharp-fanged, hungry dog. You can run at speed v, while the dog can run four times as fast.

What is your running strategy to escape the field?

Set by puzzles.nigelcoldwell.co.uk, submitted by Naran Gorsia

Answer: The strategy is to run in a circle of 0.2146R < radius < 0.25R until the dog is on the opposite side, then make for the fence like the clappers.

Other possibilities

It seems possible that there are other solutions, such as a spiral giving an angular component to your velocity. This would not work if your direction of travel was always away from the dog, (as in Θdog + π,) which was my first thought because at some point all your velocity would be angular. We could assume the dog would always move so as it would always run to try to match Θhuman. This seems solvable. You would need to consider that your radial velocity would be less than V because there is a tangental component. You could model with different angular velocities.

## Fiendish

A scientist calls an old school friend – who is an artist – to arrange a drink that evening.

The scientist, who prides himself on his accuracy, sets the time for them to meet. Both of them arrive at the correct time but the artist arrives 30 minutes earlier than his friend.

How is that possible?

Set by Pete Champ (BSc Electrical Engineering 1984)

Answer: The scientist chose the time using the 24 hour clock "22.10". His friend understood "twenty to ten".

## How to enter:

Senders of correct solutions for two or more of the puzzles will be entered into a prize draw to win a book e-voucher for the value of £10.

Congratulations to everyone who found the correct solutions and well done to our winning puzzlers:

• Martin Marriott (MSc Civil and Environmental Engineering 1981)
• Jon Tyrell (Mathematics 1974)
• Daniel Hughes (Mathematics 2014)
• Caroline Ellick (née Barnes, Agriculture and the Environment, Wye College 1999)
• Suna Bull (MBA Management 2005)
• Timothy Hartshorn (Mathematics 1966)
• Stephen Marsh (MSc History of Science, Medicine & Technology 2011)
• Hector Oti Floranes (Physics 2004)
• David Lloyd Owen (Physics 1972)
• Tabea Stoeckel (MSc Environmental Technology 2021)