Earlier today, I set a puzzle by UCLA professor Terry Tao, who is widely regarded as one of the world’s top mathematicians.

Here it is again with solutions.

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 ?

Solution

1. Day 2: 4 a + 2 b + c. Day 3: 9 a + 3 b + c

Workings: At the end of day 1 the number of coins is is a + b + c.…