Question

If in a coded language, MASTER is written as 79 7 115 121 31 109 then LAUGH will be written as
(Note: - Do NOT include any spaces in your answer)

Answer 1

Correct Answer: 7371274349

Let's find out how "MASTER" is written as "79 7 115 121 31 109" and decode the logic behind it to apply the same to "LAUGH".
Understanding the Pattern:
By comparing the positions of the letters in "MASTER" with their corresponding encoded values:
1. M (13th letter) → 79
2. A (1st letter) → 7
3. S (19th letter) → 115
4. T (20th letter)→ 121
5. E (5th letter) → 31
6. R (18th letter)→ 109
It appears there is a transformation involved. Let's break it down:
- M (13) -> 79
- A (1) -> 7
- S (19) -> 115
- T (20) -> 121
- E (5) -> 31
- R (18) -> 109
Pattern Identification:
1. M (13) -> 79
  - This might be encoded as \( 13 \times 6 + 1 \)
2. A (1) -> 7
  - This might be encoded as \( 1 \times 6 + 1 \)
3. S (19) -> 115
  - This might be encoded as \( 19 \times 6 + 1 \)
4. T (20) -> 121
  - This might be encoded as \( 20 \times 6 + 1 \)
5. E (5) -> 31
  - This might be encoded as \( 5 \times 6 + 1 \)
6. R (18) -> 109
  - This might be encoded as \( 18 \times 6 + 1 \)
This doesn't work consistently. Instead, let's consider an alternative pattern:
By using the formula \( (Position \times 6) + 1 \):
1. M (13) -> \( (13 \times 6) + 1 = 79 \)
2. A (1) -> \( (1 \times 6) + 1 = 7 \)
3. S (19) -> \( (19 \times 6) + 1 = 115 \)
4. T (20) -> \( (20 \times 6) + 1 = 121 \)
5. E (5) -> \( (5 \times 6) + 1 = 31 \)
6. R (18) -> \( (18 \times 6) + 1 = 109 \)
Now, let's apply this formula to "LAUGH":
1. L (12th letter) -> \( (12 \times 6) + 1 = 73 \)
2. A (1st letter) -> \( (1 \times 6) + 1 = 7 \)
3. U (21st letter) -> \( (21 \times 6) + 1 = 127 \)
4. G (7th letter) -> \( (7 \times 6) + 1 = 43 \)
5. H (8th letter) -> \( (8 \times 6) + 1 = 49 \)
Thus, "LAUGH" would be written as 73 7 127 43 49.

Answer 2

Instead of guessing a formula and checking it against every letter, treat the six known pairs as points on a line and find that line's equation directly, using each letter's alphabet position as \( n \) and its code as \( f(n) \).

M is the 13th letter and codes to 79, and A is the 1st letter and codes to 7. Assuming a straight-line relationship \( f(n) = mn + k \), these two points give:

\[ m = \frac{79 - 7}{13 - 1} = \frac{72}{12} = 6 \]

\[ k = 7 - 6 \times 1 = 1 \]

So \( f(n) = 6n + 1 \).

1. Check S (19th letter): \( 6 \times 19 + 1 = 115 \) — matches.
2. Check T (20th letter): \( 6 \times 20 + 1 = 121 \) — matches.
3. Check E (5th letter): \( 6 \times 5 + 1 = 31 \) — matches.
4. Check R (18th letter): \( 6 \times 18 + 1 = 109 \) — matches.

All six letters of MASTER fit \( f(n) = 6n + 1 \) exactly, confirming the rule. Now apply it to LAUGH:

1. L is the 12th letter: \( 6 \times 12 + 1 = 73 \)
2. A is the 1st letter: \( 6 \times 1 + 1 = 7 \)
3. U is the 21st letter: \( 6 \times 21 + 1 = 127 \)
4. G is the 7th letter: \( 6 \times 7 + 1 = 43 \)
5. H is the 8th letter: \( 6 \times 8 + 1 = 49 \)

So LAUGH is coded as 73 7 127 43 49.