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Cryptarithms

Stage: 3 Challenge Level: Challenge Level:1

A cryptarithm is a mathematical puzzle where the digits in a sum have been replaced by letters.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


 
AB+AB=CA 12.


 
AB+AB=BC
13.




 
AAA+BB+A=CAB 14.




 
ABC+ACB=CBA 15.




 
ABC+ABC=CDDB 16.




 
ABC+CBC=CDEB
17.




 
ABC+ABC+ABC 18.




 
ABC+ABC+ABC=BBB 19.




 
AB+BC+CA=ABC 20.




 
21.






 
A+BB+CCC=BCB 22.






 
BAA+BAA+BAA+BAA=CAAD 23.






 
ABA+ABA+ABA+ABA+ABA=CDBA    
     
 
Here is a link to a printable worksheet of this problem.


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.