RU-ALLRUSSIAN 1983 Problem 5
The positive integer k has n digits. It is rounded to the nearest multiple of 10, then to the nearest multiple of 100 and so on (n- 1 roundings in all). Numbers midway between are rounded up. For example, 1474 is rounded to 1470, then to 1500, then to 2000. Show that the final number is less than 18k/13.
Dataset text NuminaMath olympiads. Quoted with source.
Solutions
No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.