Question: In a code language January is coded as 1152337265474, how would you…

Key idea: for the nth letter in the word, add n^2 (the square of n) to the letter's alphabetical position. Concatenate those resulting numbers to get the code.

• Check with the given example JANUARY:

• J (10) + 1^2 = 11

• A (1) + 2^2 = 5

• N (14) + 3^2 = 23

• U (21) + 4^2 = 37

• A (1) + 5^2 = 26

• R (18) + 6^2 = 54

• Y (25) + 7^2 = 74

• Concatenate: 11 5 23 37 26 54 74 → 1152337265474 (matches given)

Now encode OCTOBER using the same rule:

• O (15) + 1^2 = 16

• C (3) + 2^2 = 7

• T (20) + 3^2 = 29

• O (15) + 4^2 = 31

• B (2) + 5^2 = 27

• E (5) + 6^2 = 41

• R (18) + 7^2 = 67

Concatenate these results: 16, 7, 29, 31, 27, 41, 67 → 1672931274167