The elevator problem is an observation reported by physicists Marvin Stern and George Gamow. They observed that someone who waits for an elevator (to go down) at one of the top floors (not the topmost) is more likely to see the first elevator that stops at the floor going up.
Imagine the building has 20 floors, and the person who wants to go down has her office on the 19th. The elevator is in constant flight, and it takes 1 second to cover one floor. Let’s write down a hypothetical journey.
| Floor | Up | Down |
| 20 | 5:00:38 | |
| 19 | 5:00:37 | 4:59:59; 5:00:39 |
| 18 | 36 | 5:00; 40 |
| 17 | 35 | 01 |
| 16 | 34 | 02 |
| 15 | 33 | 03 |
| 14 | 32 | 04 |
| 13 | 31 | 05 |
| 12 | 30 | 06 |
| 11 | 29 | 07 |
| 10 | 28 | 08 |
| 9 | 27 | 09 |
| 8 | 26 | 10 |
| 7 | 25 | 11 |
| 6 | 24 | 12 |
| 5 | 23 | 13 |
| 4 | 22 | 14 |
| 3 | 21 | 15 |
| 2 | 20 | 16 |
| 1 | 19 | 17 |
| 0 | 5:00:18 | 18 |
Everyone who comes between 5:00 and 5:00:37 sees the elevator going up (at 5:00:37) and only the people who reached floor 19 at 5:00:38 and 5:00:39 miss that (and only see it comes down from floor 20).
