Puzzle 1: The strange shop
To solve this puzzle, you need to find a clue in (virtual) Edinburgh: On the outside of the ICMS building, there is a blue plaque for a mathematician who gives his name to an important rule about probability. \(A\) is the year that this mathematician died.
A shop has a very strange pricing model. If you buy \(k\) items, then the price (in pence) is decided as follows:
- If \(k\) is prime, then the price is \(k\) pence.
- If \(k\) is not prime, then double \(k\) and add one:
- If the result is prime, that is the price.
- If the result is not prime, keep doubling and adding one until a prime is reached.
You enter the shop with \(A\) pence and buy 28 items.
How many pence do you leave the shop with?
Fun fact: If you try to buy 509202 items from the shop, then the shopkeeper cannot work out a price, as a prime is never reached. It is currently unknown if this is the smallest number of items that this is true for.
The answer to this puzzle is a four-digit number that scores 3 points.
Read the instructions for a reminder of what these points mean.
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This puzzle hunt was written by the team behind Chalkdust, a magazine for the mathematically curious. Find out more by reading the copy of Chalkdust in your conference pack. Talk to us after solving the puzzles about how to get an article you've written printed in our next issue.