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Scene Seen Neatly (Posted on 2010-01-10) Difficulty: 2 of 5
Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 to satisfy this alphametic equation. None of the numbers can contain any leading zero.

NEATLY = SCENE + (IT) * (IS)

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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somewhat analytical solution | Comment 2 of 3 |
As none of the numbers can have a leading zero, N=1, E=0, and S=9.

This leads to 10ATLY = 9C010 + (IT) * (I9)

Narrowing down the possibilities, we can see that:
A=(2, 3, or 4)
C=(5, 6, 7, or 8)
I=(6, 7, or 8)
L=(2, 3, 4, 5, 6, 7, or 8)
T=(2, 3, 4, 5, 6, 7, or 8)
Y=(2, 3, 4, 5, 6, 7, or 8) --- Y= 9T mod 10 ==> Y=10-T

As I is the controlling value on the right side, let's look at the possible values for I:

If I=6, A=2, C=8:
     This leaves T=(3, 4, 6, or 7), Y=10-T.
     Checking for T=3, Y=7:

     1023L7 = 98010 + (63) * (69) = 98010 + 4347 = 102357

This leads to distinct values for the nine letters:

E=0, N=1, A=2, T=3, L=5, I=6, Y=7, C=8, S=9

  Posted by Justin on 2010-01-10 19:06:13
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