### 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?

##### Stage: 3 Challenge Level:

Joshua Bull  (Brooklands Primary School, Suffolk) explains ...

I did this problem by trial and error. I worked out that D + S = E so neither D or S could be 0.
I chose at random some numbers for E and A and worked out my hundreds column first.

I found these solutions:

Are there any more solutions?

Here are some more that have been sent in.....

Alana Asher (Eastbury Farm JMI & Nursery School, Middlesex) discovered the same one as Jason's second solution.

These two came for Alicia Persaud and Priya Gami (Eastbury Farm JMI & Nursery School, Middlesex).

Here's another one from Tan Ian Wern (Tao Nan School, Singapore)

1576

+3209

--------

4785

Zachary from Clearwater Bay School in Hong Kong has found another different solution:

2548

+0917

--------

3465

Laura, Sophia and Sophie from St Michael’s Collegiate School in Hobart, Tasmania, found another different solution:

4589
+3216

--------
7805

Jayden from Elm Park School in Auckland has found another new solution:

1359
+7204
---------
8563

Well done!

Pierre Thomson from Rifton, New York, wrote to tell us that he was working on this problem with his daughter. He managed to write a computer program to find all the solutions and discovered there are 140 altogether! However, some of his solutions (like some of the above) included a zero in the thousands column - this is not how we usually write numbers so you may prefer to ignore these if you are working on this problem.