The riddle of the stolen wood

Sometimes piles of wood are marked by paint to protect them against thiefs. Continuous line is painted on the trees that are on the top of the pile, if one will steal some of them, then painted line on remaining stack will be discontinuous. To illustrate this tactic I made below picture:

The riddle of the stolen wood

If a thief would like to hide his crime, then what should he do? Present an algorithm to take n% of original trees and leave continuous red line on the remain pile.