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Brainwave 1
Happy Number 1
Did you know that numbers can be happy or sad?
Lets try and find some happy numbers by using the following process:
Choose a two digit number.
Square each of its digits and add the two squares.
Square the two digits of the answer and add the squares.
Keep repeating this process until you get an answer of 1 (happy) or the numbers are forming a repeating cycle.
Example
The number 23.
2 squared=4
3 squared=9
9+4=13
1 squared=1
3 squared=9
1+9=10
1 squared=1
0 squared=0
1+0=1
Answer = 1
Therefore 23 is a happy number.
Which two digit numbers up to 50 are happy?
Can you predict which numbers will be happy or sad?
Feature Solution
The feature solution for the problem came from 5N from Pambula PS.
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What did you have to find out?
Our class found out that the following numbers are happy numbers:
10 13 19 23 31 32 44
We also discovered that if a happy number was reversed, you would have another happy number!!
What materials did you use?
We used paper and pencils and we worked in partners then collectively shared our results.
How did you think? What strategies did you use? How did you solve this problem?
To achieve our results we used our times' tables knowledge and worked out one 2 digit number at a time.
For most numbers when the additions got to well over 100 we deduced that that number was unhappy as the pattern seem to be just getting bigger. The exception was for the number 19 which reached 100 before turning into a happy number. So we accepted the number 19 as happy:)
What answers did you come up with?
Our class found out that the following numbers are happy numbers:
10 13 19 23 31 32 44
We also predicted that 91 would be a happy number as its numerals when reversed are 19, a happy number:)
We also discovered that we are pretty clever:)
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Commendable contributors to the problem were:
Sarah & Charles; Thomas & Shannon; Sam & Nick; Samantha & Jack from Stockinbingal PS
Jai, Romie, Jaymee, Mia, Tahnee, Oliver & Taylah from Spencer PS
Year 5 from Tottenham CS
6D from Morgan Street PS
William & Anthony; Kelvin, Jenzel, Ben, Salena, Daphne & Ihsan; Jonita & Helen; Jeffrey & William; Natasha & Casey; Katherine, Jonita, Tim, Jeffrey, Frank & Chris; Andre & Renming; Sherey, Zaid, William, Anthony & Casey; Zaid from Greenacre PS
Rachel & Brandy; Ben & Jordan; Ben; Jeremy & Thomas from Sandon PS |
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Solutions were also sent in by:
Hannah, Jesse, Denali & Kirana; Laura, Ally & Lucie; Zander & Hayden; Mitch & Robert; Connie & Jamie; Jasper & Jasper from Otford PS
Clarissa; Sarah; Jessica; Stephanie; Jeremy; Emily; Skye from Wyalong PS
Rebecca, Paris & Georgia; Jenny & Anne; Celine, Shannon & Maddison; Dana & Praveena; Ingrid, Josephine & Zoe; Mikayla, Brooke & Iman from Meridan School
Andrew & Eleanor from Sir Henry Parkes Memorial PS |
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