# eLitmus Cryptarithmetic Problem – 8

## Cryptarithmetic Questions asked in eLitmus 8 Ques. For the following Cryptarithmetic find the answers to the below questions?

```           A  N  D
B  E  T
--------------
N  U  D  A
D  B  J  D
D  W  E  U
-------------------
D  A  A  J  A  A

```
 1. Which of the following set contains only even numbers ? (a) A, D, E (b) A, N, D (c) N, D, B (d) B, E, T
 2. Which of the following set contains odd numbers ? (a) A, N, D (b)  T, B, N (c) J, T, E (d) D, B, E
 3. Value of A ? (a) 1 (b) 2 (c) 3 (d) 4

It is highly suggested to go through these before solving

```Row1          A N D
Row2          B E T
Row3    ------------
Row4        N U D A
Row5      D B J D
Row6    D W E U
Row7  -------------
Row8    D A A J A A```

### Step 1

• As, D x E= _E

Hence Possible values of D and E are

At this stage you can also collect one more clue i.e. D + D = A

Now firstly take Case-1

• Case 1- E={6} then D={2, 4, 8}
• Take E=6 and D=2 Put E=6 and D=2 and rewrite the problem again.
```Row1          4 N 2 Row2          B 6 T
Row3    ------------
Row4        N U 2 A
Row5      2 B J 2 Row6    2 W 6 U
Row7  -------------
Row8    2 A A J A A```

### Step 2

• Clearly A = 4
• As from 10’s digit 2 + 2 = A
• No carry possible from previous step

Rewrite the whole problem again –

```Row1          4 N 2 Row2          B 6 T
Row3    ------------
Row4        N U 2 4 Row5      2 B J 2 Row6    2 W 6 U
Row7  -------------
Row8    2 4 4 J 4 4```

### Step 3

• Clearly T = 7
• 2 x T = _4
• Only possible for T = {2,4}
• 2 is already taken so T = 7

Let us now rewrite the problem again –

```Row1          4 N 2 Row2          B 6 7
Row3    ------------
Row4        N U 2 4 Row5      2 B J 2 Row6    2 W 6 U
Row7  -------------
Row8    2 4 4 J 4 4```

### Step 4

• Step N + B + 6 = _4
• The resultant is smaller than individual number
• ie. 6 + 2 values = _4

This is only possible when it is generating carry of 2 or 1

Carry of 2 is not possible as

• 6 + N + B = 24
• Assuming max possible values for N and B i.e. 8 and 9
• 6 + 9 + 8 gives 23

So carry should be 1 and 6 + N + B = 14

Now, 2 + W + 1(carry) = 4

• This is only possible when W = 1

Creating a sub problem now –

```Row1          4 N 2
Row2              B
Row3    ------------
Row4        2 1 6 U
```

Now, 4 x B = 21

• This is only possible when B = 5 and 1 carry from previous step

Now, rewriting the problem again –

```Row1          4 N 2 Row2          5 6 7
Row3    ------------
Row4        N U 2 4 Row5      2 5 J 2 Row6    2 7 6 U
Row7  -------------
Row8    2 4 4 J 4 4```

### Step 5

Now, U + J + U = J

Note – There is no carry from previous step.

• This is only possible when U = 0 or 5
• 5 value is already taken thus, U = 0

Clearly, N + 5 + 6 = _4

• No carry from previous step
• N = 3

Thus,

• N + 5 + 6 + 1 (carry) = 4
• Thus, N = 3

Rewriting the whole problem –

```Row1          4 3 2 Row2          5 6 7
Row3    ------------
Row4        3 0 2 4 Row5      2 5 J 2 Row6    2 7 6 0
Row7  -------------
Row8    2 4 4 J 4 4```

### Step 5

```Row1          4 3 2
Row2              6
Row3    ------------
Row5        2 5 J 2```

Clearly

• 6 x 2 = 12, thus 1 carry to next step
• 6 x 3 + 1 carry = 19
• Thus, J  = 9

Problem is solved

```Row1          4 3 2 Row2          5 6 7
Row3    ------------
Row4        3 0 2 4 Row5      2 5 9 2 Row6    2 7 6 0
Row7  -------------
Row8    2 4 4 9 4 4```

### 5 comments on “eLitmus Cryptarithmetic Problem – 8”

• KUMAR

csn anyone tell me how ti access cryptarithmetic paid materials? 0
• PrepInsta

You just go through the given link:
http://www.prepinsta.com/elitmus-online 0
• Tushar keshla

look closely,
in the second last column, it was [D D] not [D E] first you mistook it and also you have taken two different values for the alphabet E i.e. 6 and 1. 2
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•  1