Writing numbers on a segment
Source: Kvant Magazine No. 1 2020, 50th Anniversary, M233
March 10, 2023
combinatoricsnumber theoryKvant
Problem Statement
Two digits one are written at the ends of a segment. In the middle, their sum is written, the number 2. Then, in the middle between each two neighboring numbers written, their sum is written again, and so on, 1973 times. How many times will the number 1973 be written?Proposed by G. Halperin