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"Tree" Riddles - Final 6 of 126
Riddle:
There are 50 horses and 50 kings riding along an old dirt road. They came to a peach tree with 50 peaches. Each took one, yet there were still 49 left. How is this possible?
Answer: Each is the name of one of the kings and he's the only one that took one!
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.
Riddle:
A man bumps into his mathematician friend on the street whom he hasn't seen in 5 years. The man asks the mathematician how old his children are. The mathematician, who always replies in riddles said, "I now have three children. The sum of their ages is equal to the number of windows on the building in front of you and the product of their ages equals 36." The friend then says "I need one more piece of information." The mathematician then replies "My youngest child has blue eyes." What are the ages of the mathematician's three children?
Answer: They are 6, 6, and 1.
Riddle:
A forest exists somewhere on Earth. This forest has no life except for trees. After a storm, a tree was hit by lightning and falls.
What sound would it make?
Answer: None. Sound does not exist if it is unheard.
Riddle:
The names of three trees are hidden in the sentences below. The letters are in consecutive order. Can you find them? On this farm, we get ham from a hog any time. The farmer will help in every possible way. He faced two very similar choices, both bad.
Answer: Mahogany, pine and larch.
Riddle:
A woman is walking down a street night at a constant pace. As she passes the street light, she notices that her shadow becomes longer. Does the top of her shadow move faster, slower or the same when the shadow is longer as when it is shorter?
Answer: This point maintains a constant speed, independent of the lenght of the shadow.
