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# 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

**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

**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 –

**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

**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]