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

## No comments:

## Post a Comment