Three puzzles that came in from the cold

Hi guzzlers,

Every day we read stories concerning the prowess of Russian hackers. But why are they so good? A clue may lie in the fact that Russia has long excelled in maths outreach, which has been instrumental in creating a supply of people with the right skills. More of this later. Meanwhile, here are three puzzles with Russian origins.

1. *Find a solution to the equation*

28*x*+ 30*y* + 31*z* = 365

*where x, y, and z are positive whole numbers.*

2. *Place five stones on an 8×8 grid in such a way that every square consisting of 9 cells has only one stone in it.*

3. *A colony of chameleons on an island currently comprises 13 green, 15 blue and 17 red individuals. When two chameleons of different colours meet, they both change their colours to the third colour. Is it possible that all chameleons in the colony eventually have the same colour?*

The first question was told to me recently by Nikolai Andreev, of the Steklov Mathematical Institute, part of the Russian Academy of Sciences. It should take you a few seconds to solve.

The second question is taken from a fantastic after-school programme run by three Russian emigres in London. They call themselves We Solve Problems, and use two approaches used in Russia: **maths circles**, in which students can delve deeper into topics, and **maths battles**, which are like the maths equivalent of a debating society. Check out their website, where secondary school children can apply to attend weekly maths battles in London free of charge.

The third question is a stunner. It was first set in 1984 in the International Mathematics Tournament of the Towns, a wonderful maths competition founded in 1980 in Russia that now involves students in more that 100 cities and towns around the world (but mostly in Russia). The idea is to test ingenuity, rather than rote learning.

Ill be back at 5pm with the solutions and full explanations. Da? No spoilers BTL please, but do talk about great Russian mathematicians, or any experiences with Russian teaching methods.

Read more: https://www.theguardian.com/science/2017/nov/06/can-you-solve-it-secrets-of-russian-intelligence