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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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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

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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 by K Sengupta

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