IMAGE Coding Analysis

We first determine the shift in alphabetical position for each letter pair in IMAGE -> FHBNJ.

• I (position 9) to F (position 6): \( 6 - 9 = -3 \)
• M (position 13) to H (position 8): \( 8 - 13 = -5 \)
• A (position 1) to B (position 2): \( 2 - 1 = +1 \)
• G (position 7) to N (position 14): \( 14 - 7 = +7 \)
• E (position 5) to J (position 10): \( 10 - 5 = +5 \)

The derived shifts for IMAGE are: -3, -5, +1, +7, +5.

FIELD Coding Analysis

Next, we determine the shift for each letter pair in FIELD -> EMFJG.

• F (position 6) to E (position 5): \( 5 - 6 = -1 \)
• I (position 9) to M (position 13): \( 13 - 9 = +4 \)
• E (position 5) to F (position 6): \( 6 - 5 = +1 \)
• L (position 12) to J (position 10): \( 10 - 12 = -2 \)
• D (position 4) to G (position 7): \( 7 - 4 = +3 \)

The derived shifts for FIELD are: -1, +4, +1, -2, +3.

BEACH Code Pattern

The code for BEACH is formed using a specific sequence of shifts derived from the IMAGE and FIELD examples. The shifts are applied positionally:

• The 1st letter of BEACH uses the 4th shift from IMAGE (+7).
• The 2nd letter uses the 1st shift from FIELD (-1).
• The 3rd letter uses the 3rd shift from either IMAGE or FIELD (+1).
• The 4th letter uses the 5th shift from FIELD (+3).
• The 5th letter uses the 2nd shift from IMAGE (-5).

The sequence of shifts applied to BEACH is therefore: +7, -1, +1, +3, -5.

BEACH Coding Steps

Apply this derived shift sequence (+7, -1, +1, +3, -5) to the letters of BEACH:

1. B (position 2) + Shift (+7) = \( 2 + 7 = 9 \). The 9th letter is I.
2. E (position 5) + Shift (-1) = \( 5 - 1 = 4 \). The 4th letter is D.
3. A (position 1) + Shift (+1) = \( 1 + 1 = 2 \). The 2nd letter is B.
4. C (position 3) + Shift (+3) = \( 3 + 3 = 6 \). The 6th letter is F.
5. H (position 8) + Shift (-5) = \( 8 - 5 = 3 \). The 3rd letter is C.

Combining these resulting letters gives the code IDBFC.