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Cryptarithms

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
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Cryptarithms printable worksheet


A cryptarithm is a mathematical puzzle where the digits in a sum have been replaced by letters.

In each of the puzzles below, each letter stands for a different digit. 

Bearing in mind that none of the numbers below have 0 as a leading digit, can you find a solution to all of these cryptharithms?

Do any of them have more than one solution?

1.





 
A + A + A = BA 2.





 
BB+A=ACC 3.





 
AB+A=BCC 4.





 
AB+A=CDC
5.





 
AB+BC=BCB 6.





 
AB+CB=BA 7.





 
AB+CB=BBA 8.





 
AB+AB+AB+AB=CA
 
9.


 
AA+BB=CBC 10.


 
AB+AB=CBB 11.


 
12.


 
AB+AB=BC
13.




 
14.




 
ABC+ACB=CBA 15.




 
ABC+ABC=CDDB 16.




 
ABC+CBC=CDEB
17.




 
18.




 
ABC+ABC+ABC=BBB 19.




 
AB+BC+CA=ABC 20.




 
21.






 
A+BB+CCC=BCB 22.






 
BAA+BAA+BAA+BAA=CAAD 23.






 
   

     

Final Challenge

Is it possible for all of the digits 1 to 9 to appear exactly once in the addition below?

   # # #
+ # # #
   # # #


Using each digit from 1 to 9 once, what is the largest sum you can obtain in the addition above?



If you enjoyed this problem, you may also like to take a look at Two and Two.

With thanks to Don Steward, whose ideas formed the basis of this problem.

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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