### Calendar Capers

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

### Card Trick 2

Can you explain how this card trick works?

### 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.

##### 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.