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Choose any three by three square of dates on a calendar page...

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Card Trick 2

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Happy Numbers

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

Back to the Planet of Vuvv

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Why do this problem?

This problem one which requires some knowledge of both place value and different bases. Working in another base can help with real understanding of our base-$10$ number system.

You could start this by either explaining or re-visiting counting in a base such as $6$. Base $7$ could be introduced using the days of a week as an example.

Key questions

If Zios count in $3$s, what will their first 2-digit number be in human numbers?
If Zepts count in $7$s, what will their first 2-digit number be in human numbers?
What is $122, 22, 101, 41$ in Zio counting?
What is $122, 22, 101, 41$ in Zept counting?
Would drawing a sketch help with sorting out the four compass points?

Possible extension

Learners could make a similar puzzle for themselves, or go on to this similar problem: Basically.

Possible support

Suggest trying Alien Counting instead which is a simpler problem of the same type.