Riddle: If you have two quarters on a table touching each other, how can you move one of the quarters without touching it? You are only allowed to touch one quarter but not move it. You cant touch the quarter that you move. You want to get at least enough room between the two quarters to insert another coin between the two quarters.
Answer: Hold down one of the quarters very firmly. Take another coin and hit it against the quarter you are holding down. Tap hard enough to move the quarter next to it aside.
Riddle: You are in a room that is completely bricked in on all four sides, including the ceiling and floor. You have nothing but a mirror and a wooden table in the room with you.
How do you get out?
Answer: You look in the mirror you see what you saw, you take the saw and you cut the table in half, two halfs make a whole, and you climb out the hole.
Riddle: In 2000, a 40-year-old doctor told his son that when a little boy he decided to be a doctor by seeing a internet web site about performing a heart transplant on a puppy with a defective heart so that the puppy would live a normal life. I then thought that I would be a doctor so that I could help people in a similar way. What is the defect in this story?
Answer: The internet did not exist when the doctor was a little boy.
Riddle: Lazy Larry agreed to work on a job for his brother-in-law for thirty hours at eight dollars an hour, on the condition that he would forfeit ten dollars per hour for every hour that he idled. At the end of the thirty hours Larry wasn't owed any money and didn't owe his brother-in-law any money either. How many hours did Larry work and how many hours did he idle?
Answer: Lazy Larry worked 16-2/3 hours and idled 13-1/3 hours. 16-2/3 hours, at $8.00 an hour amounts to the same amount as 13-1/3 hours at $10.00 per hour.
Riddle: My first is in chocolate but not in ham, my second's in cake and also in jam, my third at tea-time is easily found, my whole is a friend who's often around. What am I?
Riddle: You're stranded in a rainforest, and you've eaten a poisonous mushroom. To save your life, you need an antidote excreted by a certain species of frog. Unfortunately, only the female frog produces the antidote. The male and female look identical, but the male frog has a distinctive croak. Derek Abbott shows how to use conditional probability to make sure you lick the right frog and get out alive. How do you get out alive?
Answer: If you chose to go to the clearing, you're right, but the hard part is correctly calculating your odds. There are two common incorrect ways of solving this problem. Wrong answer number one: Assuming there's a roughly equal number of males and females, the probability of any one frog being either sex is one in two, which is 0.5, or 50%. And since all frogs are independent of each other, the chance of any one of them being female should still be 50% each time you choose. This logic actually is correct for the tree stump, but not for the clearing. Wrong answer two: First, you saw two frogs in the clearing. Now you've learned that at least one of them is male, but what are the chances that both are? If the probability of each individual frog being male is 0.5, then multiplying the two together will give you 0.25, which is one in four, or 25%. So, you have a 75% chance of getting at least one female and receiving the antidote. So here's the right answer. Going for the clearing gives you a two in three chance of survival, or about 67%. If you're wondering how this could possibly be right, it's because of something called conditional probability. Let's see how it unfolds. When we first see the two frogs, there are several possible combinations of male and female. If we write out the full list, we have what mathematicians call the sample space, and as we can see, out of the four possible combinations, only one has two males. So why was the answer of 75% wrong? Because the croak gives us additional information. As soon as we know that one of the frogs is male, that tells us there can't be a pair of females, which means we can eliminate that possibility from the sample space, leaving us with three possible combinations. Of them, one still has two males, giving us our two in three, or 67% chance of getting a female. This is how conditional probability works. You start off with a large sample space that includes every possibility. But every additional piece of information allows you to eliminate possibilities, shrinking the sample space and increasing the probability of getting a particular combination. The point is that information affects probability. And conditional probability isn't just the stuff of abstract mathematical games. It pops up in the real world, as well. Computers and other devices use conditional probability to detect likely errors in the strings of 1's and 0's that all our data consists of. And in many of our own life decisions, we use information gained from past experience and our surroundings to narrow down our choices to the best options so that maybe next time, we can avoid eating that poisonous mushroom in the first place.