##
   ##
  ###
+ ###
 ####

In the above addition all the digits were replaced by "#".
Please restore the original numbers, given that in each column the digits form a valid arithmetic progression.

• Based upon a puzzle by Polish mathematician Marek Penshko.

I think these are the only solutions:

28 + 36 + 644 + 352 = 1060

28 + 36 + 744 + 552 = 1360

28 + 36 + 844 + 752 = 1660

74 + 63 + 652 + 441 = 1230

74 + 63 + 752 + 641 = 1530

That's based on the assumption that the constant difference in an arithmetic progression cannot be 0.  If it can, there are several (possibly many?) more solutions. 

Posted by tomarken on 2014-05-19 13:39:33