1 Year 10 Months ago

Date: 25-09-2019

# HERE = COMES – SHE, (assume S = 8). Find values of R + H + O?

PrepInsta Main

We can make this addition problem by re-writing it as –  HERE + SHE = COMES

These are the rules to solve Cryptarithmetic Questions -

1. Every Character/letter must have a unique and distinct value
2. The values of a character/letter can not be changed, and should remain same throughout
3. Starting character of number can not be zero example – 0341 should be simply 341.
4. The problem will have only and only one solution
5. Addition of two numbers is always even
6. In case of addition of two numbers, if there is carry then, the carry can only be 1
7. Once all the characters/letters are replaced with numbers, arithmetic operations must be correct

```  H E R E
+   S H E
---------
C O M E S
```

### Step 1

• C = 1 ( Rule 1, as carry is there)

Now, since –

```  H
+ _
---------
C O
```
• H + _ (nothing), can be written as H + 0 now the result of H + 0 should also be H right?
• But, the answer is coming as O, which means there must be a carry from previous step
• So, H + 1 generates a number >10 as result is C O

So, H value is 9, and O value will be H + 1 = 9 + 1 = 0 (1 carry to next step)

Rewriting the problem again

```  9 E R E
+   S 9 E
---------
1 0 M E S
```

### Step 2

• Now, they have already given S value as 8
• Now, E + E = 8, thus, E = 4

Lets find value R

• R + 9 = E
• after substituting E value R + 9 = 4
• Thus, R = 5 and (1 carry to next step)

Lets, find the value of M

• E + S + 1 (Carry) = M
• after substituting the value 4 + 8 + 1 = 3 (1 carry to next step)

The final values are –

H = 9, E = 4, R = 5, S = 8, C = 1, O = 0, M = 3

R + H + O = 5 + 9 + 0 = 14

You can check more Cryptarithmetic Questions here - https://prepinsta.com/infosys/logical/cryptarithmetic/

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