1. | Which of the following set forms a triangle ? | |||

(a) H, X, F | (b) A, P, R | (c) B, H, F | (d) H, W, X |

2. | Value of P ? | |||

(a) 4 | (b) 5 | (c) 6 | (d) 7 |

3. | Which of the following set contains only even numbers ? | |||

(a) A, B, W | (b) A, P, X | (c) A, P, R | (d) B, H, F |

```
A B W
x B P A
H X R F
F X W X
W W H H
W P H W B F
Here you don't have a single clue to start solving the Cryptarithmetic problem. You have to use Unit Digit Method ( Hit and trial approach) for solving this Cryptarithmetic problem.
Firstly read the Unit Digit Method and try to solve the problem.
```

```
1.B
2.C
3.B
A=4, B=7, W=3, P=6, H=1, X=8, R=9, F=2
4 7 3
x 7 6 4
1 8 9 2
2 8 3 8
3 3 1 1
3 6 1 3 7 2
```

```
(Solution has been given considering you as a beginner in Cryptarithmetic.)
A B W
x B P A
H X R F
F X W X
W W H H
W P H W B F
(You have to use Unit Digit Method for solving this Cryptarithmetic problem)
Firstly divide the problem in three parts for collecting the clues.
(1) A B W
x A
H X R F
(2) A B W
x P
F X W X
(3) A B W
x B
W W H H
Now analyse all the three parts separately,
In Case (3) you can see B, H, W are repeated twice.
Hence take Case (3)
(3) A B W
x B
W W H H
Now you have to start hit and trial with the possible values of H={1, 2, 3, 4, 5, 6, 7, 8, 9,0}
Firstly take H=1
Possible ways of getting 1 at Unit Digit
Case 1 W=1, B=1, H=1 Rejected (W = B = H)
Case 2 W=3, B=7, H=1 Needs to be checked
Case 3 W=7, B=3, H=1 Needs to be checked
Case 4 W=9, B=9, H=1 Rejected (W = B)
[In Cryptarithmetic, each variable should have unique and distinct values.]
You have to only check for Case 2 and Case 3
Case 2 W=3, B=7, H=1
put these values in (3) i.e.
(3) A 7 3
x 7
3 3 1 1
At this stage you can easily predict the value of A=4
Now you have to put these values in main problem and check whether it satisfies the Basic Cryptarithmetic Rules.
put W=3, H=1, A=4, and B=7
4 7 3
x 7 P 4
1 X R F
F X 3 X
3 3 1 1
3 P 1 3 7 F
Now, easily find the values of other variables.
(1) 4 7 3
x 4
1 X R F [ 1 8 9 2 ]
If you compare side by side then you will get
X=8, R=9 and F=2
Now put these values
4 7 3
x 7 P 4
1 8 9 2
2 8 3 8
3 3 1 1
3 P 1 3 7 2
Here you can easily predict the value of P=6
Hence,
4 7 3
x 7 6 4
1 8 9 2
2 8 3 8
3 3 1 1
3 6 1 3 7 2
[Relax - it's going to take some time to understand the whole concept. If you are facing any difficulty. Please go through the Cryptarithmetic Tutorial.]
```

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how to find solutn of q1?

three numbers can be sides of a triangle if and only if

sum of any two numbers > third number

solution of q1 ??

For checking the triangle go through it : http://www.wikihow.com/Determine-if-Three-Side-Lengths-Are-a-Triangle