Happy Numbers

A Maths Starter of The Day

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!

E.g. Consider 19

12 + 92 = 82
82 + 22 = 68
62 + 82 = 100
12 + 02 + 02 = 1 which means that 19 is a happy number.

How many other happy numbers can you find?

 

 

 

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Keywords: Starter | Arithmetic | Investigations

  • C R Walters, Drayton School Oxfordshire
  • Thursday, January 25, 2007
  • "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,
  • Sunday, January 28, 2007
  • "Good Idea. We have now put navigation links as you suggested at the bottom of this box. We hope this makes it easier for you to get around. Enjoy the starters,"
  • Wikipedia,
  • Wednesday, August 01, 2007
  • "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
  • Thursday, January 31, 2008
  • "One of my class wants to know if decimal numbers count. 0.1 should be ok but your tester can't cope!"
  • Transum,
  • Sunday, November 22, 2009
  • "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
  • Tuesday, January 25, 2011
  • "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! :-)."

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This starter has scored a mean of 3.8 out of 5 based on 78 votes.

 

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Answers

1, 7, 10, 13, 19, 23, 28, 31, 32, 44, 49, 68, 70, 79, 82, 86, 91, 94, 97, 100, 103, 109, 129, 130, 133, 139, 167, 176, 188, 190, 192, 193, 203, 208, 219, 226, 230, 236, 239, 262, 263, 280, 291, 293, 301, 302, 310, 313, 319, 320, 326, 329, 331, 338, 356, 362, 365, 367, 368, 376, 379, 383, 386, 391, 392, 397, 404, 409, 440, 446, 464, 469, 478, 487, 490, 496... and there are many many more!