In a coding language, if THANKS is written as 7192613168, then how POETRY is written in that code language?

Question

Prepp Team · Accepted Answer

Understanding the Coding Language Puzzle

This problem requires us to decipher a unique coding language based on a given example: the word "THANKS" is coded as "7192613168". We need to find the pattern in this encoding and then apply it to the word "POETRY". Such puzzles often involve manipulating the letters' positions in the alphabet or other simple mathematical operations.

Analyzing the Given Code for THANKS

Let's look at the word THANKS and its corresponding code 7192613168.

The word THANKS has 6 letters.
The code 7192613168 has 10 digits.

Since the number of digits is not the same as the number of letters, each letter might not correspond to a single digit. Some letters might map to one digit, while others map to two.

Let's consider the alphabetical position of each letter:

T is the 20th letter.
H is the 8th letter.
A is the 1st letter.
N is the 14th letter.
K is the 11th letter.
S is the 19th letter.

The positions are: 20, 8, 1, 14, 11, 19. The code is: 7192613168.

Let's try to find a relationship between the letter positions and the digits in the code.

A common pattern in such puzzles involves the position of letters from the end of the alphabet. Let's find the reverse alphabetical position for each letter (Reverse Position = 27 - Position from start):

T: Position 20 → Reverse Position $27 - 20 = 7$
H: Position 8 → Reverse Position $27 - 8 = 19$
A: Position 1 → Reverse Position $27 - 1 = 26$
N: Position 14 → Reverse Position $27 - 14 = 13$
K: Position 11 → Reverse Position $27 - 11 = 16$
S: Position 19 → Reverse Position $27 - 19 = 8$

The reverse positions are: 7, 19, 26, 13, 16, 8.

Now let's compare these reverse positions with the given code 7192613168:

T: Reverse Position 7. The code starts with 7.
H: Reverse Position 19. The next digits are 1 and 9.
A: Reverse Position 26. The next digits are 2 and 6.
N: Reverse Position 13. The next digits are 1 and 3.
K: Reverse Position 16. The next digits are 1 and 6.
S: Reverse Position 8. The last digit is 8.

It appears the pattern is: Each letter is mapped to its reverse alphabetical position. If the reverse position is a single digit (1-9), it's represented by that digit. If it's a two-digit number (10-26), it's represented by the two digits written sequentially.

Let's concatenate the digits based on this rule for THANKS:

T(7) → 7
H(19) → 1, 9
A(26) → 2, 6
N(13) → 1, 3
K(16) → 1, 6
S(8) → 8

Concatenated sequence: 7 then 1 then 9 then 2 then 6 then 1 then 3 then 1 then 6 then 8 = 7192613168. This perfectly matches the given code for THANKS.

Applying the Pattern to POETRY

Now, let's apply the same coding rule to the word POETRY.

First, find the alphabetical position of each letter:

P is the 16th letter.
O is the 15th letter.
E is the 5th letter.
T is the 20th letter.
R is the 18th letter.
Y is the 25th letter.

Next, find the reverse alphabetical position for each letter:

P: Position 16 → Reverse Position $27 - 16 = 11$
O: Position 15 → Reverse Position $27 - 15 = 12$
E: Position 5 → Reverse Position $27 - 5 = 22$
T: Position 20 → Reverse Position $27 - 20 = 7$
R: Position 18 → Reverse Position $27 - 18 = 9$
Y: Position 25 → Reverse Position $27 - 25 = 2$

The reverse positions are: 11, 12, 22, 7, 9, 2.

Now, convert these reverse positions into digits based on the rule (single digit for 1-9, two sequential digits for 10-26):

P(11) → 1, 1
O(12) → 1, 2
E(22) → 2, 2
T(7) → 7
R(9) → 9
Y(2) → 2

Finally, concatenate all the resulting digits in order:

1 then 1 then 1 then 2 then 2 then 2 then 7 then 9 then 2 = 111222792.

Conclusion

The code for POETRY in this language is 111222792.

Let's compare this result with the given options:

Option 1: 111222792
Option 2: 1615529025
Option 3: 112123451
Option 4: 111222893

Our calculated code matches Option 1.

Letter	Position	Reverse Position (27 - Position)	Encoded Digits
P	16	11	1, 1
O	15	12	1, 2
E	5	22	2, 2
T	20	7	7
R	18	9	9
Y	25	2	2

Concatenated Encoded Digits: 111222792.

Revision Table: Coding Language Logic

Concept	Explanation	Application in this Puzzle
Alphabetical Position	The standard position of a letter in the English alphabet (A=1, B=2, ..., Z=26).	Used to calculate the reverse position.
Reverse Alphabetical Position	The position of a letter counting from the end of the alphabet (A=26, B=25, ..., Z=1). Calculated as 27 - standard position.	The core numerical value used for encoding.
Digit Encoding Rule	How the numerical value (reverse position) is converted into digits for the code.	Single-digit reverse positions are single digits; two-digit reverse positions are sequential digits.
Concatenation	Joining the individual digits obtained for each letter into a single sequence.	Forms the final code word (e.g., 7 + 1 + 9 + ...).

Additional Information: Solving Code Language Puzzles

Coding language puzzles are a common type of logical reasoning question. They test your ability to identify patterns and rules based on examples.

Here are some strategies often used to solve them:

Alphabetical Positions: Check if the code relates to the letter's position from the start (1-26) or the end (1-26, reversed).
Vowels and Consonants: Sometimes, different rules apply to vowels and consonants.
Sum of Digits: If a number is involved (like position), its sum of digits might be used.
Difference or Sum with a Constant: The coded value might be the position plus or minus a fixed number.
Letter Pairing: Sometimes letters are paired (e.g., first with last, second with second-to-last) and a rule applies to the pair.
Skipping Letters: The pattern might involve skipping a certain number of letters.
Reverse or Jumbled Order: The letters in the word might be rearranged before encoding.

For numerical codes like the one in this problem, relating the digits back to the letter positions (forward or reverse) is a very common pattern. Always start by writing down the positions and looking for simple mathematical relationships or digit manipulations.