Can you solve it? The pals that broke the internet, ten years on

Ten years ago I published a maths olympiad question from Singapore on the Guardian website, and it changed my life.

‘Cheryl’s birthday problem’ went viral. Its unexpected success led to the birth of this column in May 2015. And here we are, almost 250 puzzles later.

The original problem, aimed at smart 14-year-olds, featured Cheryl making a statement and a subsequent conversation by Albert and Bernard. (If you want a refresh, I’ve posted it at the bottom of this page.)

The puzzle’s author, Joseph Yeo, who is senior lecturer at Singapore’s National Institute of Education, recently got back in touch. To celebrate the tenth anniversary, he has got the old gang back together, for one last hurrah.

Cheryl’s house number problem

Cheryl: I have thought of two distinct one-digit numbers. The last digit of the product of the two numbers is the last digit of Bernard’s house number. What is the sum of these two numbers?

Albert: I do not know what Bernard’s house number is.

Bernard: I know my house number, of course, and I know what the sum of the two numbers is.

Albert: At first, I did not know what the sum of the two numbers is, but now I know.

What is the sum of the two numbers?

I’l be back at 5pm UK with the solution.

NO SPOILERS. Please discuss house numbers.

As promised, this was the puzzle that kicked everything off:

Cheryl’s birthday problem

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.
Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.
Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

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.