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)
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.