Today’s column is a celebration of John Horton Conway, the legendary British mathematician, who died of coronavirus earlier this month, aged 82.

Conway was an inspirational, iconoclastic genius who invented and studied countless puzzles and games, in addition to his more highbrow work in group theory, number theory, geometry, topology and many other fields.

Born in Liverpool and educated at Cambridge he had been a professor at Princeton university since 1987. (To read more about his larger-than-life personality and his mathematical legacy, Conway was the subject of a brilliant Guardian long read in 2015. It was titled: ‘the world’s most charismatic mathematician.’)

Conway was always a font of brilliant puzzles. A few years ago I asked him if he had any suggestions for this column. He told me the two below. They are not of his own invention, but they perfectly reflect his sense of fun.

1) The Miracle Builders

I had a window in the north wall of my house. It was a perfect square, 1 metre wide and 1 metre high But this window never let in enough light. So I hired this firm, the Miracle Builders, who performed the impossible. They remodeled the window so it let in more light. When when they’d finished the window was a perfect square, 1 metre high and 1 metre wide.

How did they do it?

2) The Ten Divisibilities

I have a ten digit number, abcdefghij. Each of the digits is different, and

a is divisible by 1

ab is divisible by 2

abc is divisible by 3

abcd is divisible by 4

abcde is divisible by 5

abcdef is divisible by 6

abcdefg is divisible by 7

abcdefgh is divisible by 8

abcdefghi is divisible by 9

abcdefghij is divisible by 10

What’s my number?

[To clarify: a, b, c, d, e, f, g, h, i, and j are all single digits. Each digit from 0 to 9 is represented by exactly one letter. The number abcdefghij is a ten-digit number whose first digit is a, second digit is b, and so on. It does not mean that you multiply a x b x c x…]

I first met Conway a decade ago at a recreational maths conference in Atlanta. He was gathering pinecones and counting their spirals. The number of spirals on a pinecone is usually a Fibonacci number, but sometimes is a Lucas number. Conway was trying to find the ratio between Fibonacci and Lucas pinecones. He was easily the most distinguished mathematician in the group, yet he was also the most joyful, sharing his indefatigable, childlike curiosity about mathematical patterns with anyone who approached him.

Conway’s most famous invention was the Game of Life, a two-dimensional clockwork universe that modelled evolution and was one of the earliest computer crazes. He was always frustrated, however, that it was what he was best known for, claiming he was prouder, for example, of inventing surreal numbers.

A glider in the Game of Life.

If you ever met Conway or have been inspired by his work, please share your memories below the line.

Meanwhile, NO SPOILERS for the puzzles. I’ll be back at 5pm UK time with the solutions. (And I’ll post some hints around lunch time in the comments below.)

UPDATE: Read the puzzle solutions here.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

If you are reading this in the Guardian app, and you want a notification each time I post a puzzle, or its solution, click the ‘Follow Alex Bellos’ button above.

To read more about Conway: Genius at Play: The Curious Mind of John Horton Conway by Siobhan Roberts, is one of the most entertaining scientific biographies written in recent years.