Cryptarithmetic Problem – 3

Ques. For the following Cryptarithmetic find the answers to the below questions?

see url 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