Puzzle Playland

Two mathematicians (let's call them M and N) – once good friends – meet after a long time to have a drink together. M asks, "Are you married? Any kids? Do you still live in that old apartment building?" N replies, "Yes, I'm married with three kids, and we live in a private house now." M asks, "How old are your kids?" N replies, "Let me answer with a riddle: The product of the ages of my kids is 36. Now, see that bus over there? The sum of my kids' ages is equal to that bus number." M thinks for a moment, then says, "I don't have sufficient information to solve the puzzle." N replies, "Oh, yes, you're right. I forgot to mention that one of my kids was born before we bought the house." Soon after N provides this last bit of information, M solves the puzzle and tells N the correct ages of the kids.

Can you figure out the solution? Also, how would the solution change if N's additional piece of information was that one of his kids was born after he bought the house?

A prison warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan your strategy for the challenge I'm about to propose. But after today, you'll be in isolated cells and will have no communication with one another. In the prison is a switch room, which contains two switches labeled A and B, each of which can be in either the On or Off position. The switches aren't connected to anything. I'm not telling you the switches' present positions. After today, from time to time, whenever I feel so inclined, I'll select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must move only one of the switches. He can't move both switches, and he can't move neither switch. Then, I'll lead the prisoner back to his cell. No one else will enter the switch room until I lead the next prisoner there, and I'll instruct him to do the same thing. I'm going to choose prisoners at random. I might choose the same prisoner three times in a row, or I might jump around and come back. However, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time, if you're 100 percent certain, any one of you can declare to me, 'We have now all visited the switch room.' If that person is correct, I'll set you all free. If that person is wrong, and somebody hasn't yet visited the switch room, I'll feed you all to the alligators."

What strategy can the prisoners use to obtain freedom?

Two trains race toward each other on a railway segment that's 100 miles long. The trains are traveling at 100mph. An insect flying at 200mph flits from one train toward the other, and as soon as it arrives at the other, it flips its direction and flies back toward the first train. The insect continues bouncing back and forth between the trains until the trains crash. What's the total distance that the insect covers until the moment of the crash?

Our local toy store prices toys according to its own logic. A doll costs $17, a scooter costs $26 and a kite costs $14. Under the same system, how much will a top cost?

Kay is now 40 years old. Her son Phil is 13. How many years ago was Kay four times as old as Phil?

An interesting statement is coiled in the grid below. To spell it out, start with one letter and move to an adjacent letter in any direction.

Nick decided to test out his new bicycle for the upcoming endurance race. He rode his bike at six miles per hour and arrived in the next town one hour earlier than if he had ridden at five miles per hour. How far did he ride?