Guest Posted August 16, 2009 Report Share Posted August 16, 2009 In this alphametic, each capital letter denotes a different digit from 0 to 9, where M is nonzero and the digits 1, 2, 6 and 9 are reusable. MARILYN = 9*(MONROE) + 1926 + 1962 Determine the number that is represented by ROLE. Which 6-digit number does the word LONELY represent? Quote Link to comment Share on other sites More sharing options...
0 Pickett Posted August 19, 2009 Report Share Posted August 19, 2009 Unfortunately, I couldn't get this narrowed down very far, so I broke down and wrote a program to figure it out for me. Also, unfortunately, It appears there are a number of valid solutions: 1249758 = 9 * 138430 + 1926 + 1962 1378692 = 9 * 152756 + 1926 + 1962 1537290 = 9 * 170378 + 1926 + 1962 2149758 = 9 * 238430 + 1926 + 1962 2684907 = 9 * 297891 + 1926 + 1962 3178692 = 9 * 352756 + 1926 + 1962 3584907 = 9 * 397891 + 1926 + 1962 4078692 = 9 * 452756 + 1926 + 1962 5137290 = 9 * 570378 + 1926 + 1962 5384907 = 9 * 597891 + 1926 + 1962 6284907 = 9 * 697891 + 1926 + 1962 I haven't verified all of them by hand (to make sure my program worked...) but I did verify the first one it came up with. With the first one the answers are: 1249758 = 9 * 138430 + 1926 + 1962 0=E, 1=M, 2=A, 3=O, 4=R, 5=I, 7=L, 8=N, 9=Y ROLE = 4370 LONELY = 738079 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 21, 2009 Report Share Posted August 21, 2009 (edited) Unfortunately, I couldn't get this narrowed down very far, so I broke down and wrote a program to figure it out for me. Also, unfortunately, It appears there are a number of valid solutions: 1249758 = 9 * 138430 + 1926 + 1962 1378692 = 9 * 152756 + 1926 + 1962 1537290 = 9 * 170378 + 1926 + 1962 2149758 = 9 * 238430 + 1926 + 1962 2684907 = 9 * 297891 + 1926 + 1962 3178692 = 9 * 352756 + 1926 + 1962 3584907 = 9 * 397891 + 1926 + 1962 4078692 = 9 * 452756 + 1926 + 1962 5137290 = 9 * 570378 + 1926 + 1962 5384907 = 9 * 597891 + 1926 + 1962 6284907 = 9 * 697891 + 1926 + 1962 I haven't verified all of them by hand (to make sure my program worked...) but I did verify the first one it came up with. With the first one the answers are: 1249758 = 9 * 138430 + 1926 + 1962 0=E, 1=M, 2=A, 3=O, 4=R, 5=I, 7=L, 8=N, 9=Y ROLE = 4370 LONELY = 738079 You are indeed very very close, but there seems to be some typing errors, since an alphametic equation cannot have two or more letters to be assigned the same value. For example: 1378692 = 9 * 152756 + 1926 + 1962, implies: L= E= 6 1537290 = 9 * 170378 + 1926 + 1962, implies: I=O=7 2684907 = 9 * 297891 + 1926 + 1962, implies: L=O=9, and so on. I am confident that getting rid of these will lead to the actual solution. Edited August 21, 2009 by K Sengupta Quote Link to comment Share on other sites More sharing options...
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In this alphametic, each capital letter denotes a different digit from 0 to 9, where M is nonzero and the digits 1, 2, 6 and 9 are reusable.
MARILYN = 9*(MONROE) + 1926 + 1962
Determine the number that is represented by ROLE.
Which 6-digit number does the word LONELY represent?
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