You may also like

Double Digit

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. Try lots of examples. What happens? Can you explain it?


Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Big Powers

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Read This Page

Age 11 to 14 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:


0751   7913
+2846   +0246

3597   8159

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).

8735   5831
+0612   +0497

9347   6328


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:


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.