Problem #PRU-65334

Problems Algebra and arithmetic Number theory. Divisibility Equations in integer numbers Methods Examples and counterexamples. Constructive proofs Probability and statistics Statistics

Problem

Valerie wrote the number 1 on the board, and then several more numbers. As soon as Valerie writes the next number, Mike calculates the median of the already available set of numbers and writes it in his notebook. At some point, in Mike’s notebook, the numbers: 1; 2; 3; 2.5; 3; 2.5; 2; 2; 2; 2.5 are written.

a) What is the fourth number written on the board?

b) What is the eighth number written on the board?