eLitmus Cryptarithmetic Problem – 6
Cryptarithmetic Questions asked in eLitmus 6
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
| 1. | Find the value of G + A + S ? | |||
| (a) 12 | (b) 13 | (c) 14 | (d) 15 | |
| 2. | Find the value of 2S + R? | |||
| (a) 9 | (b) 5 | (c) 10 | (d) 12 | |
| 3. | Value of F ? | |||
| (a) 1 | (b) 2 | (c) 3 | (d) 4 | |
It is highly suggested to go through these before solving
Row1 G A S Row2 x F B I
Row3 ------------- Row4 F T B I Row5 S S T B Row6 S A S F
Row7 ---------------- Row8 S R I S T I
Step 1
- S x I= _I
- S x B= _B
- S x F= _F
As you are getting the same digit after multiplying with S (last digit). This condition is only satisfied when value of S=1. Hence, S=1
Put S=1 and rewrite the problem.
Row1 G A 1 Row2 x F B I Row3 ------------- Row4 F T B I Row5 1 1 T B Row6 1 A 1 F Row7 ---------------- Row8 1 R I 1 T I
Step 2
Dividing into subproblems –
Row1 G A 1 Row2 x B Row3 ------------- Row4 1 1 T B
Also, one more thing that we know from here is
- B + B = T
Lets start hit and trial method –
Now, you have to start hit and trial with the possible value of B={2, 3, 4, 5, 6, 7, 8, 9}
- Taking B = 2
- Thus T = 2 + 2 = 4
- Let us rewrite the problem
Row1 G A 1 Row2 x 2 Row3 ------------- Row4 1 1 4 2
Now, we can easily predict the value of A = 7
- Carry from previous step is 0
- Thus to get 4 at tens digit possible value of A needs to be either 2 or 7
- 2 x 2 = 4
- 7 x 2 = 4 (1 carry to next step)
- 2 value for A is not possible as B already 2
- Thus, A = 7
Also, clearly G = 5
- 1 Carry from previous step
- (G x 2) + = 11
- Thus, G = 5
Rewriting the whole problem
Row1 5 7 1 Row2 x F 2 I Row3 ------------- Row4 F 4 2 I Row5 1 1 4 2
Row6 1 7 1 F Row7 ---------------- Row8 1 R I 1 4 I
Step 3
Row1 5 7 1 Row2 x F Row3 ------------- Row4 1 7 1 F
- Step 5 x F = 17
- Now, this is only possible, when F = 3
- 5 x 3 + 2(carry) = 17
Rewriting the problem again –
Row1 5 7 1 Row2 x 3 2 I Row3 ------------- Row4 3 4 2 I Row5 1 1 4 2
Row6 1 7 1 3 Row7 ---------------- Row8 1 R I 1 4 I
Step 4
Clearly
- I = 3 + 1 + 1 + 1 (carry from previous step)
- I = 6
Thus, R = 8
- R = 1 + 7 (no carry from previous step)
Row1 5 7 1 Row2 x 3 2 6 Row3 ------------- Row4 3 4 2 6 Row5 1 1 4 2
Row6 1 7 1 3 Row7 ---------------- Row8 1 8 6 1 4 6
All vaues are now found
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