Happy Numbers

28 is happy

One of my favourite investigations. It is accessible for a range of abilities and offers a great lesson in the value of recording results carefully so you can use previous results and save yourself work!

Useful Links

An attractive statement of the problem on Transum

Nrich: An Excel investigation and Happy Octopus – Happy Numbers in base 8!

On TES Resources, Owen134866 has created a very clear PowerPoint to introduce the investigation.

Enter any number into Number Gossip from Tanya Khovanova for information on properties of a number including whether or not it is happy! 19 for example is happy! 

Try this Happy Number Checker on Scratch by Eulguass. Select the green flag to use the program.
Happy Numbers Scratch by Eulguass

Or get geeky with Excel – thank you MrExcel!     Happy Numbers Excel
Happy Numbers Excel calculation

Douglas Twitchell – Articles for Educators – Mathematical Fun With Happy Numbers

Happy Numbers on Kids, Code and Computer Science. Some very useful observations here.

Definition on WolframAlpha

…and a little more advanced on Wolfram MathWorld!

Some rather more advanced reading from Cornell University Library!
On the Density of Happy Numbers by Justin Gilmer

And from Numberphile

Finally – from Dr Who we have Happy Primes!