MathDB
TOT 293 1991 Spring O S3 a, b -> a+b+ab, last no from 100 remaining

Source:

June 9, 2024
algebranumber theorycombinatorics

Problem Statement

100100 numbers 11, 1/21/2, 1/31/3, ......, 1/1001/100 are written on the blackboard. One may delete two arbitrary numbers aa and bb among them and replace them by the number a+b+aba + b + ab. After 9999 such operations only one number is left. What is this final number?
(D. Fomin, Leningrad)