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?

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See the answer

Solution:

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?

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See the answer

Solution:

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

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See the answer

Solution:

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.