Happy Numbers

Some numbers are happy and others are not!

To find out whether a number is happy, square each of its digits, add the answers and repeat. If you end up with 1 the number is happy!

How many happy numbers can you find?

E.g. Consider 19

12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1

This shows that 19 is a happy number.

A Mathematics Lesson Starter Of The Day


Topics: Starter | Arithmetic | Investigations

  • C R Walters, Drayton School Oxfordshire
  • Make it so tht you can flick from day to day while on the page of one particular starter. Also have some way of knowing what date you are on while on a page - in case you want to use a starter from another day
  • Transum,
  • Good Idea. I have now put navigation links as you suggested at the top of this box. I hope this makes it easier for you to get around. Enjoy the Starters,
  • Wikipedia,
  • In the Doctor Who episode "42", a sequence of happy prime numbers is used as a code for unlocking a sealed door on a spaceship falling into a star, namely 313, 331, 367 and 379.
  • Miss Irons, Blean, Kent
  • One of my class wants to know if decimal numbers count. 0.1 should be ok but your tester can't cope!
  • Transum,
  • Sorry Miss Irons. Decimal numbers are not considered to be particularly happy though it was good of your class to be thinking about them. Perhaps your class could come up with a special name for happy decimals?
  • Primary 7, Bargeddie Primary School
  • Several of our class (Ellie, Thomas, Callum and Nicole) noticed that any numbers made up of 1 followed by any number of zeros e.g. 10, 100, 1000, 10000000, 100000000 etc.! would always be a happy number! :-).
  • Inspiring Maths, Twitter

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This starter has scored a mean of 3.3 out of 5 based on 382 votes.

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Craig Barton must surely be the voice of Mathematics teachers in the UK. His wonderful podcasts interviewing the industry experts have culminated in this wonderful book. As Craig says: "I genuinely believe I have never taught mathematics better, and my students have never learned more. I just wish I had known all of this twelve years ago..." more...

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Online Maths Shop

Laptops In Lessons

Teacher, do your students have access to computers?
Do they have iPads or Laptops in Lessons?

Whether your students each have a TabletPC, a Surface or a Mac, this activity lends itself to eLearning (Engaged Learning).

Laptops In Lessons

Here a concise URL for a version of this page without the comments.


Here is the URL which will take them to an interactive Happy Numbers activity.


Student Activity



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