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)
As none of the numbers can have a leading zero,
N=1, E=0, and
S=9.
This leads to
10ATLY =
9C
010 + (IT) * (I
9)
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=10T
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=10T.
Checking for
T=3, Y=7:
1023L
7 =
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 20100110 19:06:13 