SEND+MORE=MONEY
1) SEND + MORE = MONEY
5 4
3 2 1
S E
N D
+ M O
R E
c3 c2 c1
----------------------
M O
N E Y
1. From Column 5, M=1, since it is only carry-over possible
from sum of 2
single digit
number in column 4.
2. To produce a carry from column 4 to column 5 'S + M' is
atleast 9 so
'S=8or9' so
'S+M=9or10' & so 'O = 0 or 1'. But 'M=1', so 'O = 0'.
3. If there is carry from Column 3 to 4 then 'E=9' & so
'N=0'. But
'O = 0' so there
is no carry & 'S=9' & 'c3=0'.
4. If there is no carry from column 2 to 3 then 'E=N' which
is
impossible,
therefore there is carry & 'N=E+1' & 'c2=1'.
5. If there is carry from column 1 to 2 then 'N+R=E mod 10'
& 'N=E+1'
so 'E+1+R=E mod
10', so 'R=9' but 'S=9', so there must be carry
from column 1 to
2. Therefore 'c1=1' & 'R=8'.
6. To produce carry 'c1=1' from column 1 to 2, we must have
'D+E=10+Y'
as Y cannot be 0/1
so D+E is atleast 12. As D is atmost 7 & E is
atleast 5 (D
cannot be 8 or 9 as it is already assigned). N is atmost 7
& 'N=E+1' so
'E=5or6'.
7. If E were 6 & D+E atleast 12 then D would be 7, but
'N=E+1' & N would
also be 7 which is
impossible. Therefore 'E=5' & 'N=6'.
8. D+E is atleast 12 for that we get 'D=7' & 'Y=2'.
SOLUTION:
9 5
6 7
+ 1 0
8 5
-----------------
1 0 6
5 2
VALUES:
S=9
E=5
N=6
D=7
M=1
O=0
R=8
Y=2
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