542. A mountaineer starts rapidly climbing up a mountain trail at 6 A.M. He makes frequent and irregular stops to rest or eat. He reaches the summit at 6 P.M. At 6 A.M. the next day, he starts his way back following the same route, stopping only once to eat. He reaches the starting point at 6 P.M. Is there a point on the way where he passes at exactly the same time on both days?
543. Samantha and Suzy were squabbling over a small cake. Their mother solved the question of which one should cut it, as well as the problem of how to make sure the pieces were even, in a very simple manner. No one could complain. What was her solution?
544. A man has recently escaped from prison and is making his way home on foot. He is walking along a straight rural country lane in bright daylight. He has walked about 2 kilometers from the prison when he sees a police car coming toward him. Despite knowing that all squads would be out looking for him, he runs towards the car for a short while and turns into the forest to hide only when he is about 10 meters away from the car. Why does he run towards the police car initially?
547. When Bonnie is six years older than she is now, Bruce will be two-thirds as old as she is. When she is three times as old as she is now, Bruce will be 14. If neither one is yet a teenager, how old are they now?
551. A spider spins its web in a window frame. Each day, it spins an area equal to that of the amount already completed. It takes 30 days to cover the entire window frame. How long would two spiders take? (In the case of two spiders, each of them spins an amount equal to the area of the existing part of the web made by that particular spider.)
554. Three ladies go for an interview and the interviewer decides to test them on their reasoning abilities. They are blindfolded and are told by the interviewer that each one of them will have either a red or a blue cross painted on her forehead. When the blindfolds are removed, each lady is then supposed to raise her hand if she sees a red cross (on either of the other 2 ladies) and to drop her hand when she figures out the color of her own cross. But the interviewer blindfolds the 3 ladies and draws a red cross on each of their foreheads. The blindfolds are then removed. After looking at one another, the 3 ladies raise their hands simultaneously. After a short while, one of the ladies lowers her hands and says, "My cross is red." How did she know?