# Logic riddles

## Three children

Johnny‘s mother had three children. The first child was named April. The second child was named May. What was the third child‘s name?
Johny.
69.23 %

## The same birthday

What is the least number of people that need to be in a room such that there is greater than a 50% chance that at least two of the people have the same birthday?
Only 23 people need to be in the room. Our first observation in solving this problem is the following: (the probability that at least 2 people have the same birthday + the probability that nobody has the same birthday) = 1.0 What this means is that there is a 100% chance that EITHER everybody in the room has a different birthday, OR at least two people in the room have the same birthday (and these probabilities don't add up to more than 1.0 because they cover mutually exclusive situations). With some simple re-arranging of the formula, we get: the probability that at least 2 people have the same birthday = (1.0 - the probability that nobody has the same birthday) So now if we can find the probability that nobody in the room has the same birthday, we just subtract this value from 1.0 and we'll have our answer. The probability that nobody in the room has the same birthday is fairly straightforward to calculate. We can think of this as a "selection without replacement" problem, where each person "selects" a birthday at random, and we then have to figure out the probability that no two people select the same birthday. The first selection has a 365/365 chance of being different than the other birthdays (since none have been selected yet). The next selection has a 364/365 chance of being different than the 1 birthday that has been selected so far. The next selection has a 363/365 chance of being different than the 2 birthdays that have been selected so far. These probabilities are multiplied together since each is conditional on the previous. So for example, the probability that nobody in a room of 3 people have the same birthday is (365/365 * 364/365 * 363/365) =~ 0.9918 More generally, if there are n people in a room, then the probability that nobody has the same birthday is (365/365 * 364/365 * ... * (365-n+2)/365 * (365-n+1)/365) We can plug in values for n. For n=22, we get that the probability that nobody has the same birthday is 0.524, and thus the probabilty that at least two people have the same birthday is (1.0 - 0.524) = 0.476 = 47.6%. Then for n=23, we get that the probability that nobody has the same birthday is 0.493, and thus the probabilty that at least two people have the same birthday is 1.0 - 0.493) = 0.507 = 50.7%. Thus, once we get to 23 people we have reached the 50% threshold.
69.22 %

## The thunder comes before the lightning

The thunder comes before the lightning; the lightning comes before the clouds. The rain dries everything it touches. What am I?
A volcano.
69.22 %

## Girl's B-day

A girl was ten on her last birthday, and will be twelve on her next birthday. How is this possible?
Today is her 11th Birthday.
69.19 %

## Five Men Like Pete

Pete is a worker on a large ship with hundreds of other men. He is constantly making mistakes, tying ropes the wrong way, steering the ship the wrong way, and making other blunders. One time he accidentally caused the ship to get stuck in a shallow shore, causing thousands of dollars in damage. However, when Steve, the captain of the ship, is asked about Pete, Steve says "I wish we had five men like Pete on this ship." Why would he say this?
Unfortunately for the ship, there are dozens of men who are as inept as Pete is. Captain Steve wishes there were FEWER men like Pete on the ship, since there are currently far more than five.
68.97 %

## I can only live where there is light

I can only live where there is light, but I die if the light shines on me. What am I?
68.70 %

## Nut with a whole

I am a nut with a whole. What am I?
Donut.
68.60 %

## I cannot be seen

I repeat only the last word you say. The more I repeat, the softer I got. I cannot be seen but can be heard. What am I?
An Echo.
68.57 %

## My nose is called a snout

I have a little tail. My nose is called a snout. I live on a farm. I can say, "Oink-oink" I am a...
Pig.
68.38 %