Can you solve it? A headful of PINs

When it comes to choosing PIN numbers for our bank cards or our phones, the most popular numbers are the obvious ones , such as 1234, 1111, 1212 etc, according to what you read on the web.

Today’s puzzle is about what is the best strategy when you choose the digits randomly.

Perplexing PINs

You and a friend are discussing how you choose four-digit PINs. You establish that neither of you would ever use the digit 0.

“I like to choose four different random digits,” you say.

“I like to choose three different random digits,” they reply, “so one of the digits is used twice.”

Which strategy gives the largest pool of possible four-digit PINs?

I’ll be back at 5pm UK with the solution. Meanwhile, NO SPOILERS.

Instead, please discuss your favourite PIN numbers, passwords and randomisation strategies.

Thanks to Mayo Marriott for suggesting today’s puzzle.

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.

I’m the author of several books of maths and puzzles, and also the co-author with Ben Lyttleton of the children’s book series Football School. The latest in the Football School series is The Greatest Ever Quiz Book, out now!

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.