The number on the door is a map. At 222 East 34th Street the last two digits are the residence line, 01 through 31. Everything in front of those two digits is the floor. Residence 1204 is floor 12, line 04. Residence 504 is the same line on floor 5.

Floor first, line second
Low floors print as three digits. High floors print as four. The line does not change. If you like the plan for 1507, 1807 and 2307 are the same line, not a new search. Ask for the floor plan of that line before you walk the hallway.
Listings on this site use the residence number. So do the floor-plan PDFs. If a broker flyer uses a different label, match it to the number on the door before you compare square footage.
The same line is not always the same apartment
The building changes configuration at floor 18. Line 04 is the clean example: a studio of 480 square feet on floors 5 through 17, a two-bedroom of 797 square feet on floors 18 through 22, then a three-bedroom on 23 and 24. Same last two digits. Different rooms. Do not assume 804 and 1804 are interchangeable because the number looks similar.
Other lines may hold the same plan from 5 to 24. The floor plan is the proof, not the number. If two residences share a line and the plans do not match, trust the plan.
How to use it on a tour
Write down the line you like. Then ask which floors of that line are actually available, and on what date. A vacant unit on a line you already rejected is not a second chance at the plan you wanted. Filter current listings by the number, or schedule a tour and ask for that line. Call (212) 684-3222.
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