AoPS - Problem

The answer is $\fbox{Yes}.$ Assume WLOG that the pastries are, in counterclockwise order, 7 meat, 7 cabbage, and 1 cherry. If her first guess is the cherry, she's done. Otherwise, WLOG she chose a cabbage, and therefore will only guess counterclockwise (vice versa for meat). She can then skip three pastries counterclockwise. If it is another cabbage, she can skip one pastry; if this is cherry, she is done; if it's meat, the one she skipped is cherry; if it's cherry, the next one in counterclockwise order is cherry. Otherwise, assume her second guess is meat. She can choose the pastry in the middle of her first two guesses (skip one clockwise); if it's cherry, she's done; if it's meat, the next pastry clockwise is cherry; if it's cabbage, the next pasty counterclockwise is cherry.