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# eLitmus Cryptarithmetic Multiplication Questions

## Multiplication Probelms Cryptarithmetic for eLitmus

**eLitmus Cryptarithmetic problems are generally asked in eLitmus exam and are of high difficulty. You can study most important questions for eLitmus Cryptarithmetic from below –**

J E B B ---- J E J E A -------- B A D E Assume that E = 4

1. | Value of 5B? | |||

(a) 15 | (b) 10 | (c) 5 |

2. | Value of B + A? | |||

(a) 7 | (b) 5 | (c) 1 | (d) 8 |

3. | Value of D ? | |||

(a) 4 | (b) 3 | (c) 7 | (d) Can not be determined |

It is highly suggested to go through these before solving - Cryptarithmetic Introduction - How to Solve Cryptarithmetic Problems

Row 1 J E Row 2 B B Row 3 ---- Row 4 J E Row 5 J E A Row 6 -------- Row 7 B A D E Assume that E = 4

### Step 1

- Clearly, from the Row 2 row where
- B is written in common multiplication
- J E is multiplied with B and results in B, which results in J E.
- Thus, the B value is 1

### Step 2

- In Row 4 : E + A = E.
- This, only possible when A value is 0

Row 1 J E Row 2 1 1 Row 3 ---- Row 4 J E Row 5 J E 0 Row 6 -------- Row 7 1 0 D E

### Step 3

- Now in Row 5 and Row 7
- J + nothing(Row 4) gives us 10.
- Thus, there must be 1 carry from the previous step and J value must be 9
- Now, the problem looks like-

Row 1 9 E Row 2 1 1 Row 3 ---- Row 4 (carry)1 9 E Row 5 9 E 0 Row 6 -------- Row 7 1 0 D E

#### Step 4

- 9 + E = D
- Now, from the previous step, there can not be any carry
- As E + 0 = E, and E can have values between E = {0,9}
- Max value of E can be 8 as J = 9 (already taken)

- Thus, step 9 + E = D will have no carry from the previous step
- However, this is generating carry to the next step
- Thus, 9 + E = D + 10
- E – D = 1
- The only thing that we can conclude is that E and D are consecutive but we can’t deduce their value.

### Cryptarithmetic Questions asked in eLitmus 2

**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 **

H O W x C U T ---------- D D C P D W P W D U O A ---------------- D C E P D P

1. | Value of T + O + P ? | |||

(a) 3 | (b) 8 | (c) 6 | (d) 9 |

2. | Value of B ? | |||

(a) 1 | (b) 2 | (c) 3 | (d) 4 |

3. | Value of 2C ? | |||

(a) 13 | (b) 13 | (c) 17 | (d) 11 |

It is highly suggested to go through these before solving - Cryptarithmetic Introduction - How to Solve Cryptarithmetic Problems

As, W x U= _ W [ D W P W ] For W the probablities are- Case-1 When W={2, 4, 8} and U={6} For W the probablities are- Case-2 When W={5} and U={3, 7, 9} Taking the first scenerio Take U=6 and problem looks like, H O W x C 6 T ———- D D C P D W P W D 6 O A

—————- D C E P D P

Getting more progress, H O W x C 6 T ---------- D D C P D W P W D 6 O A ---------------- D C E P D P D + 6 + (carry) = C [Carry may be either 0, 1 or 2] Hence, problem looks like of C= {7, 8, 9} Start hit and trail C={7, 8, 9} and W={2, 4 ,8} C=7 and W=2 when C=7 and W=2 then D=9 [ As, C + W = D] If we take take D=9 then, H O W x C 6 T ---------- D D C P 9 W P W 9 6 O A ---------------- 0 C E P D P

D=0 and D=9 two values of D this C=7 and W=2(Not true) Now, Check the with other possible values of W and C Let's take C=7 and W=4 then D=1 as C + W = D [last digit] Taking D=1, C=7 and W=4 now problems looks like H O 4 x 7 6 T ---------- 1 1 7 P 1 4 P 4 1 6 O A ---------------- 1 7 E P 1 P Now, you can easily predict the value of A=8 As, 7 x 4= _ A [last digit] H O 4 x 7 6 T ---------- 1 1 7 P 1 4 P 4 1 6 O 8 ---------------- 1 7 E P 1 P Now, H O 4 x 7 ---------- 1 6 O 8 You can easily predict the value of H=2 2 O 4 x 7 6 T ---------- 1 1 7 P 1 4 P 4 1 6 O 8 ---------------- 1 7 E P 1 P

Now you can easily predict other values. Value of T=5 O=3 and P=0 2 3 4 x 7 6 5 ---------- 1 1 7 0 1 4 0 4 1 6 3 8 ---------------- 1 7 9 0 1 0

H=2, O=3, W=4, C=7, U=6, T=5, D=1, S=0, E=9 2 3 4 x 7 6 5 ------------ 1 1 7 0 1 4 0 4 1 6 3 8 ---------------- 1 7 9 0 1 0

### Cryptarithmetic Questions asked in eLitmus 3

**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 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

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