### 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?

### 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?

### Card Trick 2

Can you explain how this card trick works?

# Back to the Planet of Vuvv

##### Stage: 3 Challenge Level:

Martha in Year 5 at Hatherleigh Primary School has sent us a very well explained solution to this tricky problem. She says:

First I counted up to $122$ in base $3$ and base $7$. Then I marked them off in fives in base $10$.

Here is her working:

She goes on to say:

After that I wrote down the four numbers we were given, found out what they were in base $3$ and $7$, and worked out whether or not they could be made out of $7$s and $3$s:

$22$ and $41$ could only be in base $7$ so the other two were Zios. So:

West - Zio
East - Zept
South - Zio
North - Zept