# IMO Challenge

Solve an IMO-style problem and win £1000!

G-Research are delighted to be Gold Sponsors of the 60th International Mathematical Olympiad hosted in Bath.

To celebrate our support of the IMO, we are launching a series of IMO-style problems for a chance to win £1,000 each week.

We will post a taster problem here on Monday 1st July to get you warmed up, then every Monday at midday, from 8th July until 22nd July, we will publish a new prize challenge on this page.

The first person to submit the correct answer to challenge@gresearch.co.uk will win £1,000.

## Taster problem

To get you warmed up, here is a taster problem. This is just for fun – prizes begin next week. And be warned, this is a little easier than our prize challenges…Good luck!

## Challenge One:

***UPDATE***

We have a winner! Zhuan Koh from LSE was the first to submit the correct answer and wins £1000. Congratulations Zhuan!

Many thanks to all the people who submitted their answers. If you would still like to have a go for fun to see if you got the puzzle right, feel free to submit your working to challenge@gresearch.co.uk and we will let you know how you got on.

Here is the original puzzle:

Nim* is a game similar to Nim, with one difference: there is a single ‘passing token’ which either player may take in lieu of their turn if it is still available. Once either player takes the passing token the game plays exactly like a normal game of Nim. The game ends when there are no stones left, regardless of whether or not the passing token has been taken. The game is played under normal play convention, ie the last player to make a move wins.

The initial state contains the passing token in addition to piles of size 1, 3, 5, . . . , 2019.

Can the first player force a win? If so, how? If not, how can player two force a win?

## Challenge Two:

***UPDATE***

We have a winner! Kim Ngan Nguyen from UEA was the first to submit the correct answer and wins £1000. Congratulations Kim!

Many thanks to all the people who submitted their answers. And don’t forget to come back at midday on Monday 22nd July for our final challenge!

## Challenge Three:

***UPDATE***

We have a winner! Zsuzsanna Baran from University of Cambridge was the first to submit the correct answer and wins £1000. Congratulations Zsuzsanna! Thank you to everyone who has taken part in all our challenges over the past four weeks!