# Cryptarithmetic Problem - 3

Ques. For the following Cryptarithmetic find the answers to the below questions?
```         P  O  P
M  U  T
---------
S  O  I  U
G  M  T  U
U  I  R  O
-----------------
U  U  S  M  U  U
```
 1. Value of G + U + T ? (a) 10 (b) 12 (c) 6 (d) 9
 2. Value of S + G ? (a) 3 (b) 9 (c) 7 (d) 8
 3. Value of  2U ? (a) 4 (b) 6 (c) 8 (d) 2
```It is evendent from row 2 that for multiplication U x P = U. So U cannot be 1. Also since,
I + U = U. So I = 0. Now from the 10000th addition, 1 + G + (I)0 = A. So G = 1 and U = 2.```
```         P  O  P
M  2  T
---------
S  O  0  2
1  M  T  2
2  0  R  O
-----------------
2  2  S  M  2  2
Simlarly from 2nd row of mul. 2 x P = 2, Also from first row of T x P = 2.

So P should take 6, and T should take 7. (These are the only possibilities)
If E= 6, then P x T = 6 x 7 = 42. So 4 carry over.  Now 7 x O + 4 = 0. So O = 8.

```
```         6  8  6
M  2  7
---------
S  8  0  2
1  M  7  2
2  0  R  8
-----------------
2  2  S  M  2  2

Now S = 4 as 7 x 6 + 6 = 48.  Also M = 3. R =5
This would be the solution

```
```         6  8  6
3  2  7
---------
S  8  0  2
1  3  7  2
2  0  5  8
-----------------
2  2  4  3  2  2

G = 1, U = 2, T = 7, R = 5, S = 4, O = 8, E = 6```