In: Computer Science
CHECK + THE = TIRES
Solve this puzzle using constraint satisfaction and draw the constraint graph.
Given, CHECK + THE = TIRES
We have constraints as
i) No two letters have same value
ii) Sum of digits must be shown in the problem
iii) The values must be in range on (0-9)
C H E C K
+ T H E
T I R E S
Let consider a table having letter( which are given in the equation) and digits which are agined after solving.
Letters | Value (digits) |
C | 5 |
H | 9 |
E | 4 |
K | 3 |
T | 6 |
I | 9 |
R | 1 |
S | 7 |
Note : The digits coloumn has been filled after solving the problem.
Solution:
Note : The Answer is displayed first as a picture please take that as a reference and follow the steps
Step1 :
Let us start from the lest side of the answer
The C and T are in same phase so there must be a carry over C to get the diifferent value for T
So in CHECK from left to right after C we have H to get the carry on C the value of H must be 9 So let us freeze 9 for H and as H is 9 and the answer letter for H is I,
We have H=9 If there is a carry then the value will become 10 so I = 0 and remaining carry will be farwarded to C
Step 2:
Consider, H from THE whose value is 9 let us consider C=5,
C+H = E
5+9 = 4 and one carry (14)
So Value for E=4
As C=5 then in the left most side the TIRES T = 6 since C+ carry =T ----> 5+1(carry) = 6
So T=6
Step 3 :
In CHECK E=4
In THE T=6
C+T = R
5+6 = 1 and carry 1 (11)
So R =1
Step 4 :
In the right most part E = 4
The ramaining values are K and S Which are non repeatable so you can consider any value which is noot going to give a carry.
I took K=3
So K+E=S
3+4=7
So S=7.
Considering these steps fill the digits coloumn in the table alternatively.
Thank you.