Logical Reasoning

Coding/Decoding

Hard

According to a coding scheme the sentence

Peacock is designated as the national bird of India is coded as

$5688999351135556678564581366668913347913366$

This coding scheme has the following rules:

The scheme is case-insensitive (does not distinguish between upper case and lower case letters).

Each letter has a unique code which is a single digit from among $1,2,3, \ldots, 9$ .

The digit $9$ codes two letters, and every other digit codes three letters.

The code for a word is constructed by arranging the digits corresponding to its letters in a non-decreasing sequence.

What best can be concluded about the code for the letter B?

1 or 3 or 4

3 or 4

✅ Correct Option: 3

Slide 1/10

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

We can see that code for word "BIRD" is 1334.

1 corresponds to D and one 3 corresponds to I.

Hence, we can say that code for letters 'R' and 'B' are '3' and '4' in any order.

Therefore, we can say that for letter 'B' there are two possible numbers: 3 or 4.

B and R is coded as 3 or 4.

Question 5

What best can be concluded about the code for the letter L?

Question 7

For how many digits can the complete list of letters associated with that digit be identified?

Question 8

Which set of letters CANNOT be coded with the same digit?

What best can be concluded about the code for the letter B?

Solution

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