# Cryptarythmatic with Forward Checking, MRV, and Least Constraining Value

Question: Solve the cryptarythmetic problem in Figure 6.2 by hand, using the strategy of backtracking with forward checking and the MRV and least-constraining-value heuristics.

In a cryptarythmetic problem, each of the letters are unknown numbers; usually different ones.
The C variables are carries, so one mathematical sentence that occurs will be
O + O = R * X_1, where O and R are between 0 and 9 inclusive, and X_1 has the domain { 0, 1 }.

I'm trying to understand how to approach this problem with "backtracking with forward checking and the MRV and least-constraining-value heuristics."
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Commented:
In solving by hand, how would you describe the methods you use, without worrying about the names of the techniques?
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Author Commented:
Backtracking: "The term backtracking search is used for a depth first search that chooses values for one variable at a time and backtracks when a variable has no legal moves left to assign."

Forward checking: "Whenever a variable X is assigned, the forward-checking process establishes arc-consistency for it: for each unassigned variable Y that is connected to X by a constraint, delete from Y's domain any value that is inconsistent with the value chosen for X."

MRV: Most constrained variable. "It also has been called the 'most constrained variable' or 'fail-first' heuristic, the latter because it picks a variable that is most likely to cause a failure soon, thereby pruning the search tree. If some variable X has no legal values left, the MRV heuristic will select X and failure will be detected immediately- avoiding pointless searches through other variables."

Least-constraining-value: "Once a variable has been selected, the algorithm must decide on the order in which to examine its values. For this, the least-constraining-value heuristic can be effective in some cases. It prefers the value that rules out the fewest choices for the neighboring variables in the constraint graph."
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Commented:
I'm not asking for the definition of the terms, I'm asking what you do when you solve cryptarythmetic problems by hand.
However, since you mentioned those techniques, do you recognize any similarity with what you do?
Could the way you solve them by hand be made more efficient by applying those principles?
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Author Commented:
I've forgotten the diagram:
Diagram.PNG
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Commented:
Can you fill in the constraints?
Is that the way you would solve it by hand?
Does seeing the constraints that way make the hand solution easier?
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Author Commented:
A description of how I would solve this cryptarythmatic problem without any other instructions:

Assign 7 to T.
Therefore, C_3 = 1, F = 1, and O = 4.
Assign 3 to W.
Therefore, U = 6 and C_2 = 0.
O + O = R = 8, with C_1 = 0.
T was revised from 9 to 7.

In all, T = 7,   W = 3,
O = 4,   F = 1,
U = 6,   R = 8,
X_1 = 0, X_2 = 0, and X_3 = 1.
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Author Commented:
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Author Commented:
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Author Commented:

Commenter (Ozo) did not respond to my message. Even something like "I don't know" would have been better than nothing.
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