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.
