Ivan and Mirka were sharing pears from a plate. Ivan always took two pears, and Mirka took half of what was left on the plate. They proceeded in this manner: Ivan, Mirka, Ivan, Mirka, and finally Ivan, who took the last two pears.

Determine who ended up with more pears and by how many.

(M. Dillingerová)

Hint. How many pears did Mirka take the second time?
Ivan took three times two pears, in the end, he had 6 pears. To determine how many pears Mirka ended up with, we will trace back the changes in the number of pears step by step. $\mathrm{K}$ to do this, it is enough to realize that before each of Ivan's takings, there were two more pears on the plate, and before each of Mirka's takings, there were twice as many pears on the plate.

Ivan took the last 2 pears during his third taking.

Mirka took 2 pears during her second taking, before that, there were 4 pears on the plate. Ivan took 2 pears during his second taking, before that, there were 6 pears on the plate.

Mirka took 6 pears during her first taking, before that, there were 12 pears on the plate. Ivan took 2 pears during his first taking, originally, there were 14 pears on the plate. Mirka took a total of 8 pears, so in the end, she had two more pears than Ivan.