# Cryptarithmetic Problem - 2

```                H  O  W
x  C  U  T
----------
D  D  C  P
D  W  P  W
D  U  O  A
----------------
D  C  E  P  D  P```
 1. Value of T + O + P ? (a) 3 (b) 8 (c) 6 (d) 9
 2. Value of B ? (a) 1 (b) 2 (c) 3 (d) 4
 3. Value of  2C ? (a) 13 (b) 13 (c) 17 (d) 11
```
As, W x U= _ W [ D W P W ]
For W the probablities are-

Case-1 When W={2, 4, 8} and U={6}
For W the probablities are-

Case-2 When W={5} and U={3, 7, 9}
Taking the first scenerio
Take U=6 and problem looks like,

H  O  W
x  C  6  T
----------
D  D  C  P
D  W  P  W
D  6  O  A
----------------
D  C  E  P  D  P
```
```Getting more progress,

H  O  W
x  C  6  T
----------
D  D  C  P
D  W  P  W
D  6  O  A
----------------
D  C  E  P  D  P

D + 6 + (carry) = C    [Carry may be either 0, 1 or 2]
Hence, problem looks like of C= {7, 8, 9}
Start hit and trail C={7, 8, 9} and W={2, 4 ,8}

C=7 and W=2
when C=7 and W=2 then D=9 [ As, C + W = D] If we take take D=9 then,

H  O  W
x  C  6  T
----------
D  D  C  P
9  W  P  W
9  6  O  A
----------------
0  C  E  P  D  P```
```D=0 and D=9 two values of D this C=7 and W=2(Not true)
Now, Check the with other possible values of W and C
Let's take C=7 and W=4

then D=1 as C + W = D [last digit]
Taking D=1, C=7 and W=4 now problems looks like
H  O  4
x  7  6  T
----------
1  1  7  P
1  4  P  4
1  6  O  A
----------------
1  7  E  P  1  P
Now, you can easily predict the value of A=8  As, 7 x 4= _ A [last digit]

H  O  4
x  7  6  T
----------
1  1  7  P
1  4  P  4
1  6  O  8
----------------
1  7  E  P  1  P
Now,
H  O  4
x  7
----------
1  6  O 8
You can easily predict the value of H=2

2  O  4
x  7  6  T
----------
1  1  7  P
1  4  P  4
1  6  O  8
----------------
1  7  E  P  1  P```
```Now you can easily predict other values.
Value of T=5 O=3 and P=0

2  3  4
x  7  6  5
----------
1  1  7  0
1  4  0  4
1  6  3  8
----------------
1  7  9  0  1  0```
```H=2, O=3, W=4, C=7, U=6, T=5, D=1, S=0, E=9

2  3  4
x  7  6  5
------------
1  1  7  0
1  4  0  4
1  6  3  8
----------------
1  7  9  0  1  0```