Solution
Understanding the set :-
In this set, You are given a sentence and its corresponding coded version, with the following rules:
- Rules of the Scheme
a) Case- insensitive : Letters like P and p are treated the same.
So "Peacock" = "peacock".
- Unique Letter-to-Digit Mapping:
Each letter of the alphabet is assigned a unique digit between 1 and 9.
So, each letter always maps to the same digit, no matter where it appears.
- Distribution of Letters to Digits:
One digit (9) represents only 2 letters.
All other digits (1–8) each represent 3 letters.
Since there are 26 letters in the alphabet:
8 digits × 3 letters = 24
1 digit (9) × 2 letters = 2
Total = 24 + 2 = 26 ( accounts for all letters)
- How Each Word is Coded:
For every word in the sentence:
Replace each letter with its assigned digit.
Then sort the digits in non-decreasing order.
This sorted string of digits becomes the code for that word.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| I | S |
For India -
It is coded as 13366.
Now, we know, in "India" there are 2 I's
=> I will represent either 3 or 6.
For Also, as we can see, 'IS' is coded as 35.
=> I will be coded as 3.
=> S will be coded as 5.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| A | I | S |
Now, as we can see "AS" is coded as 56.
And, we know, S is coded as 5.
=> A will be coded as 6.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| A | I | S | F | O |
Now, there is O is common in both "of" and "national".
Now, OF is coded as - 79
and, NATIONAL is coded as - 13666689
Both of them only has only 9 is common.
=> O is coded as 9.
=> F is coded as 7.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| A | I | S | F | O, C |
Clue 3 says,
The digit 9 codes two letters
We know, one of them is O.
Now, in peacock code there are three 9's.
Remaining two O's will be represented by the same letter.
We can see that only letter 'C' has appeared twice in Peacock.
Therefore, we can say that 'C' is assigned number '9'.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| A, D | I | S | N | F | O, C |
In word national 'N' has appeared twice.
In code only digit '6' has appeared more than once.
Hence, we can say that code of letter N is '6'.
Consequently, we can say that code for letter 'D' is '1' because in India rest of the numerals are already taken.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| A, D | I | S | N | F, T | O, C |
In words, 'the' and 'national' only letter 'T' is common.
In code as well only digit '8' is common in two codes.
Hence, we can say that letter code for letter 'T' is 8.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| A, D | I, H | E | S | N | F, T | O, C |
In words, 'the' and 'peacock' only letter 'e' is common.
In code as well only digit '5' is common in two codes.
Hence, we can say that letter code for letter 'e' is 5.
Consequently, we can say that leftover letter, in word "the", 'H's code is 4.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| A, D , L | I, H | E | S | N | F, T | O, C |
We can see that code for word "NATIONAL" is 13666689.
Hence, we can say that code for the letter L is '1'.
| Peacock | is | designated | as | the | national | bird | of | India |
|---|---|---|---|---|---|---|---|---|
| 5688999 | 35 | 1135556678 | 56 | 458 | 13666689 | 1334 | 79 | 13366 |
| Letters | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| A, D , L | I, H | E | S | N | F, T | O, C |
Digit '1' is used for L and D only.
We can not figure out the third letter for which digit 1 is used.
Digit '2' is not used for any letter.
Hence, we can not figure out all the letters for which digit 2 is correct code.
Digit '3' is used for letter 'I' only. Hence, we can not figure out all the letters for which digit 3 is correct code.
Digit '4' is used for letters 'H' and one of 'B' and 'R'.
Hence, we can not figure out all the letters for which digit 4 is correct code.
Digit '5' is used for letters 'S' and 'E'.
We can not figure out the third letter for which digit 5 is used.
Digit '6' is used for letters 'A' and 'N'.
We can not figure out the third letter for which digit 6 is used.
Digit '7' is used for letters 'G' and 'F'.
We can not figure out the third letter for which digit 7 is used.
Digit '8' is used for letters 'T', 'P' and K.
Hence, we can say that this is one of the digit for which the complete list of letters associated is known.
Digit '9' is used for letters 'C' and 'O'.
Hence, we can say that this is one of the digit for which the complete list of letters associated is known.
Therefore, we can say that for only two digits (8 and 9), the complete list of letters associated is known.