Today’s puzzle is set by Terence Tao, who may be the world’s most famous mathematician.

Tao, aged 51, has been a global phenomenon since the age of ten, when he became the youngest competitor at the International Maths Olympiad, a record he still holds. For the last three decades he has been a professor at UCLA, where he has been garlanded with prizes, and where one of his colleagues famously said: “Terry is like Mozart: mathematics just flows out of him.”

Tao is a very visible leader of the field, not only because of his scientific contributions and collaborations, but also because he writes the most widely-read blog in research level maths. When Open AI earlier this month stunned the community with the release of hundreds of proofs of long-standing open questions – the “mathpocalypse” – his blog has become one of the most important forums for the community’s response.

This week Tao publishes Six Maths Essentials, his first work aimed at a general audience. The puzzle below reflects ideas in the book.

He said: “I like this puzzle in that it naturally introduces algebraic ways of thinking as the most efficient way to solve the problem: working out small examples by hand can give some valuable initial intuition, but it will be algebra that lets you solve the entire problem in a civilized amount of time.”

The magic money plant

In an online game, you earn coins by harvesting from plants. There are two types of plant:

  • a regular plant produces a single coin per day

  • a mother plant produces a single coin and two seeds per day. (A seed will grow into a regular plant the following day.)

At the start of the game, a player has a certain number of mother plants, regular plants and coins, but not more than nine of each.

Suppose that I begin on Day 1 with a mother plants, b regular plants and c coins.

1. How many coins do I have in total at the end of days 2 and 3?

2. Find an expression for how many coins I have at the end of Day X.

3. At the end of Day 10 I have 427 coins. What are a, b and c?

I’ll be back at 5pm UK with the solutions – and Tao will explain what it all means.

PLEASE NO SPOILERS Instead discuss the mathpocalypse.

UPDATE: The solutions can be read here.

Six Maths Essentials by Terence Tao is out tomorrow. You can buy it at the Guardian Bookshop.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.