MathDB
an insect jumping on [0,1]

Source: Iran TST 2023 ; Exam 2 Problem 2

March 16, 2023
IranTSTIranian TSTcombinatorics

Problem Statement

Suppose 12<s<1\frac{1}{2} < s < 1 . An insect flying on [0,1][0,1] . If it is on point aa , it jump into point a×s a\times s or (a−1)×s+1(a-1) \times s +1 . For every real number 0≤c≤10 \le c \le 1, Prove that insect can jump that after some jumps , it has a distance less than 11402\frac {1}{1402} from point cc.
Proposed by Navid Safaei
Back to ProblemsView on AoPS