You *may* be able to use this to get out of the lease, if you act quickly. First, it goes without saying that if you physically visited the building prior to leasing, you could not: in that case, you would have had direct, personal knoweldge of the (to say the lease) unusual floor-numbering system and by renting after that, you would be held to have waived, or given up, an objection to it.But if you did not visit the building so this came as a surprise, then this might be a case of either fraud (if we assume that numbered, advertised, etc. to deliberately mislead people) and/or "mutual mistake"--there was no agreement as to what was being leased between you and the building, because you thought you were leasing a 16th-floor aparment while they thought they were leasing you one that was 8 floors up. (For there to be a vaid contract, like a lease, the two sides have to agree on what is being done.) Since higher floors are generally more expensive and desirable (better views, further from street noise, etc.), a difference of 8 floors is a material, or important one. So an 8-floor difference due to either mutual mistake or fraud could allow you out of the lease. But if you wait too long, you'll be considered to have accepted the unit and given up the right to object.