Mathematics is often thought of as a straightforward subject, like one and one equals two. But it can also involve paradoxes and puzzles, and for the first lesson we will look at and discuss some mathematical puzzles.
Mathematics seems to be at the heart of reality. Neptune was found after Urbain Le Verrier predicted its position after calculating mathematically where it should be. Eistein's formulas for relativity predicted an expanding universe, but he didn't believe it. It was only when observational evidence showed it really was expanding that Einstein accepted his own math. So if you can manipulate math, you can manipulate reality.
We will discuss some of the following puzzles (I may substitute others, or add more if we get through these), and I want you to give your answer (if there are multiple possible answers, just give one), your reasoning for the answer, and any flaws you might think you see in other answers (be polite!):
A man is on a bear hunt. He sees a bear about 100 yards (or metres) due east of him, he panics and runs 100 yards/metres due north, regains his composure, turns, sees the bear has not moved from where it had been and shoots due south killing the bear. What color was the bear?
Three men go out to lunch. The bill is $30, so each of the men gives the waiter a $10 bill. The waiter soon realizes the total should have been $25, and goes to take a $5 bill back to the men, but, thinking that that doesn't split easily between the three, he pockets two dollars and takes three $1 bills back to the men. Each of the men have now paid $9 each, totalling $27, the waiter has pocketed $2, giving a total of $29. Where has the other dollar gone?
A wizard flies from point A to point B, a distance of 2 miles, at a speed of 15 mph. He immediately turns around and flies back. What speed must he do on the return trip to average 30 mph over the complete flight (out and back)?
A frog is at the bottom of a 10' well. Every hour it climbs 3', pauses and slips back 2'. How long does it take the frog to climb out?
A ship is tied up at the dock, and it has a ladder down the side with rungs at 6" spacing. At the start the water is just below the level of the bottom step. The tide is coming in and the water is rising 4" every ten minutes. How many rungs will be covered in 2 hours?