Ready to test your little grey cells?

Imperial’s best minds set the ultimate puzzle challenge.

1. Hard

A farmer puts a heap of potatoes on his weighing scales, finding that it weighs 100lb. Unknown to him, it consists of 99 per cent water and one per cent solids by weight. He then carries out other farm work, leaving the heap in the sun so that its water content gradually evaporates, until it is 98 per cent water by the time he returns.

What is the weight of the heap when he returns?

See the answer


50 lbs.

At the beginning, 1 lb of solids comprises one per cent of the weight, so the total weight is 100 lb. At the end, the 1 lb of solids comprises two per cent of the weight, so the total weight is 50 lb.

2. Very hard

Noting their order, but hiding them from you, I place two aces and a jack face down in a row. You must identify an ace by pointing to one of the cards and asking me a single yes/no question. However, if you have pointed to an ace, I will answer truthfully, but if you have pointed to the jack, I will answer yes or no at random.

What card do you point to and what question do you ask?

See the answer


Point to the middle card and ask ‘is the card to the left an ace?’

If the answer is 'yes', choose the left card. If the answer is 'no', choose the right card.

3. Fiendish

A computer glitch meant that all punctuation marks had been deleted from the following line of text. Replace the punctuation so that it makes sense:

Jane where John had had had had had had had had had had had the teachers approval

See the answer


Jane, where John had had “had”, had had “had had”. “Had had” had had the teacher’s approval.

How to enter

Senders of correct solutions for two or more of the puzzles will be entered into a prize draw to win a signed copy of Professor David J Hand's new book Dark Data: Why What You Don’t Know Matters.

Entries are now closed.

With thanks to Professor David Hand, Emeritus Professor of Mathematics and Senior Research Investigator, Faculty of Natural Sciences.

Congratulations to the first ten respondents who contacted us with two or more correct solutions from the issue:

  • Alexander Dean (MSci Physics with Theoretical Physics 2018)
  • Dr Faye Karampapa (MEng Civil Engineering 2001)
  • Paul Holt (BSc Physics 1983)
  • Caroline Ellick (BSc Agriculture and the Environment, Wye College 1999)
  • Robert Maciejczek (BSc Physics 1991)
  • Stewart Bean (BSc Chemistry 1975)
  • Shengqin Yang (MSc Advanced Materials Science and Engineering 2015)
  • Kathryn Sayer (MEng Mechanical Engineering 2016)
  • Pete Champ (BEng Electrical Engineering 1984)
  • David Rowe (BSc Chemistry 1984)