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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?

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Repeaters

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.

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Digit Sum

What is the sum of all the digits in all the integers from one to one million?

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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)

   1576

+3209

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  4785

 

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

  2548

+0917

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  3465

 

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

  4589
+3216

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  7805


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

  1359
+7204
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  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.