Understanding the Coding Pattern

The question asks to find the code for 'HBSFOO' given that 'GARDEN' is coded as 'HBSFOO'. This implies we need to find the pattern used to convert 'GARDEN' to 'HBSFOO' and then apply the same pattern to 'HBSFOO'.

Step 1: Analyze GARDEN to HBSFOO Conversion

Let's compare the letter positions in the alphabet (A=1, B=2, ... Z=26) and find the shift for each letter:

• G (7) becomes H (8): Shift = $8 - 7 = +1$
• A (1) becomes B (2): Shift = $2 - 1 = +1$
• R (18) becomes S (19): Shift = $19 - 18 = +1$
• D (4) becomes F (6): Shift = $6 - 4 = +2$
• E (5) becomes O (15): Shift = $15 - 5 = +10$
• N (14) becomes O (15): Shift = $15 - 14 = +1$

The sequence of shifts is: +1, +1, +1, +2, +10, +1.

Step 2: Apply the Pattern to HBSFOO

Now, apply the same sequence of shifts (+1, +1, +1, +2, +10, +1) to the letters of 'HBSFOO':

• H (8) + 1 = I (9)
• B (2) + 1 = C (3)
• S (19) + 1 = T (20)
• F (6) + 2 = H (8)
• O (15) + 10 = Y (25)
• O (15) + 1 = P (16)

Step 3: Determine the Coded Word

Combining the resulting letters, the code for 'HBSFOO' is 'ICTHYP'.