This document summarizes a lecture on artificial intelligence topics including game theory, constraint satisfaction problems, and cryptarithmetic problems. It provides examples of solving cryptarithmetic problems by assigning digits to letters to make the arithmetic equations valid. The lecture covered optimal decision making in games, tree search algorithms, constraint propagation techniques, and backtracking search approaches for solving constraint satisfaction problems. Example problems and step-by-step solutions of cryptarithmetic equations were presented to illustrate the constraint satisfaction framework.

1. AI3391 ARTIFICAL INTELLIGENCE
(II YEAR (III Sem))
Department of Artificial Intelligence and Data
Science
Session 22
by
Asst.Prof.M.Gokilavani
NIET
1/24/2024 Department of AI & DS 1

2. TEXTBOOK:
• Artificial Intelligence A modern Approach, Third Edition,
Stuart Russell and Peter Norvig, Pearson Education.
REFERENCES:
• Artificial Intelligence, 3rd Edn, E. Rich and K.Knight
(TMH).
• Artificial Intelligence, 3rd Edn, Patrick Henny Winston,
Pearson Education.
• Artificial Intelligence, Shivani Goel, Pearson Education.
• Artificial Intelligence and Expert Systems- Patterson,
Pearson Education.
1/24/2024 Department of AI & DS 2

3. Topics covered in session 22
1/24/2024 Department of AI & DS 3
• Game theory
• optimal decision in games
• alpha beta Search
• Monte Carlo tree search
• stochastic games
• partially observed games
• Constraint satisfaction problem
• Constraint propagation
• Backtracking search for CSP
• Local search for CSP
• structure of CSP.

4. Cryptarithmetic Problem
• Cryptarithmetic Problem is a type of constraint
satisfaction problem where the game is about digits and
its unique replacement either with alphabets or other
symbols.
• In cryptarithmetic problem, the digits (0-9) get
substituted by some possible alphabets or symbols.
• The task in cryptarithmetic problem is to substitute
each digit with an alphabet to get the result
arithmetically correct.
• We can perform all the arithmetic operations on a given
cryptarithmetic problem.
1/24/2024 4
Department of AI & DS

5. Constraints for cryptarithmetic
problem
• Unique digit to be replaced with a unique alphabet
(no repeated digits).
• The result should satisfy the predefined arithmetic
rules, i.e., 2+2 =4
• Digits should be from 0-9 only.
• In addition operation only one carry forward.
• The problem can be solved from both sides,
i.e., lefthand side (L.H.S), or right-hand side
(R.H.S)
1/24/2024 5
Department of AI & DS

6. Example 1
• Given a cryptarithmetic problem, i.e., S E N D
+ M O R E = M O N E Y.
1/24/2024 6
Department of AI & DS

7. Step 1
1/24/2024 7
Department of AI & DS
• Starting from the left hand side (L.H.S) , the terms
are S and M. Assign a digit which could give a
satisfactory result. Let’s assign S->9 and M->1.
Hence, we get a satisfactory result by adding up the
terms and got an assignment for O as O->0 as well.

8. Step 2
• Now, move ahead to the next terms E and O to
get N as its output.
1/24/2024 8
Department of AI & DS
Adding E and O, which means 5+0=0, which is not
possible because we cannot assign the same digit to
two letters.

9. • Add carry 1 to the value E to change the
value of alphabet.
1/24/2024 9
Department of AI & DS

10. Step 3
1/24/2024 10
Department of AI & DS
• Further, adding the next two terms N and R we get,
But, we have already assigned E->5. Not possible with 5 to E
Again, after solving the whole problem, we will get a
carryover on this term, so our answer will be satisfied.

11. Step 4
• Again, on adding the last two terms, i.e., the
rightmost terms D and E, we get Y as its result.
1/24/2024 11
Department of AI & DS

12. • Keeping all the constraints in mind, the final resultant
is as follows:
1/24/2024 12
Department of AI & DS
Alphabets Values
S 9
E 5
N 6
D 7
M 1
O 0
R 8
Y 2

13. Example 2
1/24/2024 13
Department of AI & DS

14. Example 3
1/24/2024 14
Department of AI & DS

15. Topics to be covered in next session 23
• Backtracking CSP’s
Thank you!!!
1/24/2024 Department of AI & DS 15