











eLitmus Cryptarithmetic Problem – 3
Cryptarithmetic Questions asked in eLitmus 3
Important
The Cryparithmetic methods discussed below are developed by PrepInsta only and available on 2 PrepInsta owned websites only. Anyone copying the method will be legally sued as these are not open source but are PrepInsta's Proprietary methods


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) 3 | (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 highly suggested to go through these before solving
Row 1 P O P Row 2 M U T Row 3 --------- Row 4 S O I U Row 5 G M T U - Row 6 U I R O - - Row 7 ----------------- Row 8 U U S M U U
Step 1
- As I + U = U
- This is only possible when, I = 0
- Also, there can not be a carry from previous step as
- Max values of U can be 9. Thus, no carry over.
Thus I = 0
Row 1 P O P Row 2 M U T Row 3 --------- Row 4 S O 0 U Row 5 G M T U - Row 6 U 0 R O - - Row 7 ----------------- Row 8 U U S M U U
Step 2
Read Rule 3 here before next step
- P x U = _U
- Can also be written as
- U x P = _U (is of form X x Y = _X)
According to Rule 3, this is only possible when –
- P = {6} & U = {2, 4, 8}
- U = {5} & P = {3, 7, 9}
Let us try for values (P,U) = (6, 2) and start hit and trial method –
Replace all the values and start hit and trial again –
Row 1 6 O 6 Row 2 M 2 T Row 3 --------- Row 4 S O 0 2 Row 5 G M T 2 - Row 6 2 0 R O - - Row 7 ----------------- Row 8 2 2 S M 2 2
Step 3
After replacing with assumed hit and trial values –
- 6 x T = _2
- This is only possible when T = 7
- As 6 x 7 = 42
- As of now, it doesn’t cause any conflict this, moving further, we create the sub problem as this –
Row 1 6 O 6 Row 2 2 Row 3 --------- Row 4 G M 7 2 Note - 0(digit) and O(alphabet) are different.
- 6 x 2 = GM
- We can easily predict the following
- G is 1 as 6 x 2 results in 12
- M is 2 + carry (from previous step)
Also,
- O x 2 + 1(carry from previous step 6 x 2) = _7
- Possible values for O can be 3 or 8
If, O = 3
- 6 X 2 = GM
- O x 2 from previous step is 3 x 2 = 6
- This, doesn’t generate any carry from previous step, thus, M = 2
- This is not possible as U value is already assumed to be 2
Let us try with O = 8
- O x 2 will generate 1 carry to next step as result will be 17 (1 carry from previous step)
- Thus, 6 X 2 + 1 carry = GM
- M = 3 and G = 1
Rewriting the question again
Thus,I = 0 M = 3, G = 1, O = 8, P = 6, U = 2, T = 7 till now
Pending values are S R
Row 1 6 8 6 Row 2 3 2 7 Row 3 --------- Row 4 S 8 0 2 Row 5 1 3 7 2 - Row 6 2 0 R 8 - - Row 7 ----------------- Row 8 2 2 S 3 2 2
Step 4
R value can be found out as follows with this sub problem
Row 1 6 8 6 Row 2 3 Row 3 --------- Row 4 2 0 R 8
- 6 x 3 from units places gives 18 and 1 carry to next step
- 8 x 3 from tens places gives us 24 + 1 (Carry from previous step) this 25
- Value of R = 5
Thus, I = 0, G = 1, U = 2, M = 3, R = 5, P = 6, , T = 7, O = 8, till now
Finally, finding the value of S is also very easy
S = either 9 or 4.
We do hit and trial and find out its 4.
Options do not match with the solution. None of the options are correct for 1 and t
For any questions about eLitmus Cryptarithmetic questions email us at PrepIn[email protected]