CROSS
+ ROADS
DANGER
A value can be assigned to only one alphabet .....values are 0-9
Constraint -
+ ROADS
DANGER
A value can be assigned to only one alphabet .....values are 0-9
Constraint -
- S+S = R
- S+D+C1 = E1 [C1=CARRY]
- O+A+C2 = G
- R+O+C3=N
- C+R+C4=A
- D=C5
As values are between 0 and 9, the maximum carry that can be generated is 1.
therefore, D=C5=1
Inference -
S+S=R
2S=R
therefore, R=even={0,2,4,6,8}
S= {0,1,2,3,4}
but S is not equal to 0 because if this happens, S=0 and R=0 ( not possible)
S is not equal to 1 as D=1
S = {2,3,4}
Propagation -
- Let S=2 than R=4, E=3 ,now to generate a carry D, these terms don't agree , therefore, S is not equal to 2.
- Let S=3 than R=6, E=4 ,A and O can't be zero(0), because if O is zero than A=G , if A is zero than O=G , Let O=2 than N=8 , Let A=5 than G=7 , Now, if D=1, C is to be 9 Therefore, the solution is :-
9 6 2 3 3
C R O S S
6 2 5 1 3
+ R O A D S
1 5 8 7 4 6
D A N G E R