Choose any three by three square of dates on a calendar page...
Can you explain how this card trick works?
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.
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)
Zachary from Clearwater Bay School in Hong Kong has found another different solution:
Laura, Sophia and Sophie from St Michael’s Collegiate School in Hobart, Tasmania, found another different solution:
Jayden from Elm Park School in Auckland has found another new solution:
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.