In a certain code, the word STOP is written as 5827, similarly, the word DROP…

Concept

In a set-based number-coding puzzle, a code word's digits form an unordered set that corresponds to the unordered set of its letters — the position of a digit inside the code need not mirror the position of the matching letter inside the word. When two code words share a letter, that letter's digit must lie in the intersection of the two words' digit-sets. Chaining these intersections across every pair of words that share a letter pins down individual letter-to-digit values one at a time.

Application

1. STOP → digit set {5, 8, 2, 7}; DROP → digit set {2, 9, 6, 8}. The letters common to STOP and DROP are O and P, so {O, P} = STOP ∩ DROP = {2, 8}.

2. STOP → {5, 8, 2, 7}; TED → {5, 4, 6}. The only letter common to STOP and TED is T, so T = STOP ∩ TED = {5}, giving T = 5.

3. DROP → {2, 9, 6, 8}; TED → {5, 4, 6}. The only letter common to DROP and TED is D, so D = DROP ∩ TED = {6}, giving D = 6.

4. DROP's full digit set is {2, 9, 6, 8}. Removing the digits already assigned — {O, P} = {2, 8} and D = 6 — leaves R = 9.

5. TED's full digit set is {5, 4, 6}. Removing T = 5 and D = 6 leaves E = 4, confirming every TED digit is accounted for.

6. PORT is built from the letters P, O, R, T, so its digit set is {2, 8} ∪ {9} ∪ {5} = {2, 5, 8, 9}.

Cross-check

Compare {2, 5, 8, 9} against the digit sets of the four options: 8295 → {2, 5, 8, 9} (exact match); 8265 → {2, 5, 6, 8} (carries a stray 6); 8945 → {4, 5, 8, 9} (carries a stray 4). Only one option is built from exactly the required four digits, which settles the code even though the internal split between O and P is not independently pinned down by the given words.

So the code for PORT is 8295.