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Calendar Capers

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat this for a number of your choice from the second row. You should now have just one number left on the bottom row, circle it. Find the total for the three numbers circled. Compare this total with the number in the centre of the square. What do you find? Can you explain why this happens?

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Reverse to Order

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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Card Trick 2

Can you explain how this card trick works?

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.