Problem Decomposition: Goal Trees, Rule Based Systems, Rule Based Expert Systems. Planning: STRIPS, Forward and Backward State Space Planning, Goal Stack Planning, Plan Space Planning, A Unified Framework For Planning. Constraint Satisfaction : N-Queens, Constraint Propagation, Scene Labeling, Higher order and Directional Consistencies, Backtracking and Look ahead Strategies.

1. Topic To Be Covered:
Crypt-Arithmetic Problem in AI
Jagdamba Education Society's
SND College of Engineering & Research Centre
Department of Computer Engineering
SUBJECT: Artificial Intelligence & Robotics
Lecture No-13(UNIT-02)
Prof.Dhakane Vikas N

2. Crypt-Arithmetic Problem in AI
What is Crypt-Arithmetic Problem in AI???
 It is type of constrained satisfaction problem in Ai
 The Crypt-Arithmetic problem in Artificial Intelligence is a type of
encryption problem in which the written message in an alphabetical form
which is easily readable and understandable is converted into a numeric
form which is neither easily readable nor understandable.
 In simpler words, the crypt-arithmetic problem deals with the converting
of the message from the readable plain text to the non-readable cipher
text.
 The constraints which this problem follows during the conversion is as
follows:

3. Crypt-Arithmetic Problem in AI
What is Crypt-Arithmetic Problem in AI???
The rules or constraints For a crypt-arithmetic problem are as follows:
 There should be a unique digit to be replaced for a unique alphabet.
 Digits should be from 0-9 only.
 There should be only one carry forward, while performing the addition
operation on a problem.
 The problem can be solved from both sides, i.e., left-hand side (L.H.S), or
right-hand side (R.H.S) .
 There must be only on solution to problem.
 Numbers must not begin with zero(e.g.0234 it is incorrect).
 Numerical base is 10 to be considered if required
 The result should satisfy the predefined arithmetic rules, i.e., 2+2 =4,
nothing else.

4. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic
problem as well as its constraints
better with the help of an example:
Example:-01(TO+GO=OUT)
STEP-01:
-These alphabets are replaced by numbers
such that all the constraints are satisfied. So
initially we have all blank spaces.
-We start from leftmost side ,there we have
leftmost symbol is:O
-It is the letter which is generated by carrying.
So, carry generated can be only one. SO, we
have O=1.
-When we are doing addition of n letters &
result of adding of letters is n+1 letters ,then
resulted letter value is always 1 as carry.
LETTER DIGIT
T
O 1
G
U

5. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic
problem as well its constraints better
with the help of an example:
Example:-01(TO+GO=OUT)
STEP-02:
-Next we have T+G=U & O+O=T
-We will go for O+O=T first.
-We have o=1, so O+O(1+1)=2(T)
LETTER DIGIT
T 2
O 1
G
U

6. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic
problem as well its constraints better
with the help of an example:
Example:-01(TO+GO=OUT)
STEP-03:
-Next we have T+G=U
-We T=2
-So,2+G=U
-Now here, We know U must generate carry
so,2+G Must be 10 or Greater that 10
-Means we must add such number in 2 so,
that it we can get carry generated(or we can
addition 10 or more than 10)
LETTER DIGIT
T 2
O 1
G
U

7. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic
problem as well its constraints better
with the help of an example:
Example:-01(TO+GO=OUT)
STEP-03:
-Now here, We know U must generate carry
so,2+G Must be 10 or Greater that 10
-Means we must add such number in 2 so, that
it we can get carry generated(or we can
addition 10 or more than 10)
-We have first Option(If we consider G=9):2+G
as 2+9(G)=11,her we get U=1
-But we cant chose U=1 as 1 is already assigned
to O.
-
LETTER DIGIT
T 2
O 1
G
U

8. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic
problem as well its constraints better
with the help of an example:
Example:-01(TO+GO=OUT)
STEP-03:
-We have second Option(If we consider
G=8):2+G as 2+8(G)=10,her we get U=0
-Which can be chosen & then we can tally the
answer as follows:
2 1
+ 8 1
-------------------
1 0 2
LETTER DIGIT
T 2
O 1
G 8
U 0

9. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic problem
as well its constraints better with the help of
an example:
Example:-02(SEND+MORE=MONEY)
STEP-01:
-These alphabets then are replaced by numbers
such that all the constraints are satisfied. So
initially we have all blank spaces.
-We start from leftmost side ,there we have
leftmost symbol is:M
-It is the letter which is generated by carrying.
So, carry generated can be only one. SO, we
have M=1.
-When we are doing adding of n letters & result
of adding of letters is n+1 letters ,then resulted
letter value is always 1 as carry.
LETTER DIGIT
S
E
N
D
M 1
O
R
Y

10. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic problem
as well its constraints better with the help of
an example:
Example:-02(SEND+MORE=MONEY)
STEP-02:
-Next we have S+M=O,WE KNOW M=1 ,SO WE
We have equation s+1=o(here s+m=O has to
generate carry as we have M=1)
-When s=8 ,carry cant be generated (as 8+1=9)
-Only when S=9 carry can be generated so we
have (9+1=10) and hence S=9 & O=0
LETTER DIGIT
S 9
E
N
D
M 1
O 0
R
Y

11. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic problem
as well its constraints better with the help of
an example:
Example:-02(SEND+MORE=MONEY)
STEP-03:
-Next we have E+O=N(here we have O=0)
-if we do E+0=N(In this case we are having E &
N having same value as anything get added in 0
result will be 0 only.)
-But we cant have E & N with same value
,according to constraint of cryptarithmatic
-So ,there must be carry generated above E,
which will get added at E.
-So, here we assume E+0+1=N i.e. E+1=N(N &
E are differ by 1)—exp(1)
LETTER DIGIT
S 9
E
N
D
M 1
O 0
R
Y

12. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic problem
as well its constraints better with the help of
an example:
Example:-02(SEND+MORE=MONEY)
STEP-04:
-Next we N+R=E
-Now here addition of N & R must generate
carry as we have assume carry need to be
generated above E.
-So, we need to add such a two numbers such
that they can generate carry, here we cant use
9 number as it is already used.
-So, we can have relation as follow
-N+R=E+10(10,here to represent carry)
-But there might be carry as well over the N so,
we write relation as N+R(+1)=E+10exp(2)
LETTER DIGIT
S 9
E
N
D
M 1
O 0
R
Y

13. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic problem
as well its constraints better with the help of
an example:
Example:-02(SEND+MORE=MONEY)
STEP-04:
--N+R=E+10(10,here to represent carry)
-But there might be carry as well over the N so,
we write relation as N+R(+1)=E+10— exp(2)
-So now we substitute expression(1) in exp(2)
-we get E+1+R(+1)=E+10
-If here we don’t consider carry R=9
-which is not possible because S=9
-so we need to consider carry her & so R=8
-We still cant have value of N so we go forward.
LETTER DIGIT
S 9
E
N
D
M 1
O 0
R 8
Y

14. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic problem
as well its constraints better with the help of
an example:
Example:-02(SEND+MORE=MONEY)
STEP-05:
--R=8
-We still cant have value of N so we go forward.
-Next we have D+E=Y has to be such that ,it
can generate carry because we have know carry
has to be generated above N
-Here we know Y must be greater than 11
because 0 and 1 value already taken for O and
M.
-So possibilities are 7+6 or 7+5
-If we take 7+5=12(D=7 & E=5 ,so Y=2)
-N=6
LETTER DIGIT
S 9
E 5
N 6
D 7
M 1
O 0
R 8
Y 2

15. Crypt-Arithmetic Problem in AI
Let’s understand the crypt arithmetic problem
as well its constraints better with the help of
an example:
Example:-02(SEND+MORE=MONEY)
STEP-05:
-
9 5 6 7
+ 1 0 8 5
---------------------------------
1 0 6 5 2
LETTER DIGIT
S 9
E 5
N
D 7
M 1
O 0
R 9
Y 2