Days or sleeps until Christmas? What’s the difference?

Activity Sheets

How many days until Christmas – or how many sleeps? What’s the difference?

“How many sleeps” sounds a bit childish but it’s far less confusing than how many days.
Why?  It’s the old fencepost problem – so popular in maths questions and quizzes.

Look at the timeline below for the 21st to the 25th of December.

The “sleeps” are the fenceposts; the days are the spaces in between.

fenceposts

Imagine it is the 21st of December…

If you are looking at the fenceposts or sleeps, then all day on the 21st of December, you can see quite clearly that there are 4 fenceposts or sleeps to pass and then it will be Christmas Day.

If you are looking at the days, it’s not so clear. If you are looking at days, there are 3 full days (midnight to midnight or fencepost to fencepost) between now and Christmas Day. If it’s morning, should you count the 21st as well, making 4 days until Christmas? What do you do in the afternoon? Or evening?

It’s the same diagram, same problem, we’re just changing the way we look at it – the fenceposts or the spaces in between.

If it doesn’t fit your image to say “5 sleeps till Christmas” when you’re at the office or down the pub, or if you’re a shiftworker, call your fenceposts “midnights” because that’s even more precise and keeps the focus firmly on the posts.

So, this website says “sleeps” instead of “days” until Christmas. I hope that makes it clearer for you, and it will save me thinking “is that really right” every time I look at it.

Suggested  Activity:
This is a common mathematical problem. Find other examples where this confusion arises. Why do you think it’s referred to as a “fencepost” problem?

More Advanced Activity:
Try to write a simple computer program, or formula in a spreadsheet, which calculates fenceposts needed for any given length of fence.