Can you solve it? A magical melody from the Mozart of math

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.”

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.

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.