5

Part of 2022 Indonesia Regional

Problems(1)

As Inefficient As Possible

Source: Indonesia RMO 2022, Essay No 5 (Modified from Mathematical Excalibur 510)

1

22

are written on a board. A "move" is a procedure of picking two numbers

a,b

on the board such that

b \geq a+2

a

b

to be replaced with

a+1

b-1

. Determine the maximum possible number of moves that can be done on the board.

IndonesiaRMO2022mathematicalexcaliburcombinatorics