There are 4 big houses in my home town. They are made from these materials: red marbles, green marbles, white marbles and blue marbles.
Mrs Jennifer's house is somewhere to the left of the green marbles one and the third one along is white marbles.
Mrs Sharon owns a red marbles house and Mr Cruz does not live at either end, but lives somewhere to the right of the blue marbles house.
Mr Danny lives in the fourth house, while the first house is not made from red marbles.
Who lives where, and what is their house made from ?
From, left to right:
#1 Mrs Jennifer - blue marbles
#2 Mrs Sharon - red marbles
#3 Mr Cruz - white marbles
#4 Mr Danny - green marbles
If we separate and label the clues, and label the houses #1, #2, #3, #4 from left to right we can see that:
a. Mrs Jennifer's house is somewhere to the left of the green marbles one.
b. The third one along is white marbles.
c. Mrs Sharon owns a red marbles house
d. Mr Cruz does not live at either end.
e. Mr Cruz lives somewhere to the right of the blue marbles house.
f. Mr Danny lives in the fourth house
g. The first house is not made from red marbles.
By (g) #1 isn't made from red marbles, and by (b) nor is #3. By (f) Mr Danny lives in #4 therefore by (c) #2 must be red marbles, and Mrs Sharon lives there.
Therefore by (d) Mr Cruz must live in #3, which, by (b) is the white marbles house. By (a) #4 must be green marbles (otherwise Mrs Jennifer couldn't be to its left) and by (f) Mr Danny lives there.
Which leaves Mrs Jennifer, living in #1, the blue marbles house.
Alone I am 24th, with a friend I am 20.
Another friend and I am unclean.
What am I?
The letter 'X'. It is the 24th letter of the alphabet, XX in Roman numerals is 20, and XXX is a label for movies that are very inappropriate (unclean).
Even though the odds are always in favor of the gambling house, why does the establishment insist on a house limit on stakes?
Every casino in the world would go bankrupt without a house limit on stakes. Without it, gamblers would keep doubling their stakes until they won. No matter how bad a losing streak they were on, they would eventually win. For more information, search: Martingale
We all know that square root of number 121 is 11. But do you know what si the square root of the number "12345678987654321" ?
111111111
Explanation:
It's a maths magical square root series as :
Square root of number 121 is 11
Square root of number 12321 is 111
Square root of number 1234321 is 1111
Square root of number 123454321 is 11111
Square root of number 12345654321 is 111111
Square root of number 1234567654321 is 1111111
Square root of number 123456787654321 is 11111111
Square root of number 12345678987654321 is 111111111 (answer)
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.
Emperor Akbar once ruled over India. He was a wise and intelligent ruler; and he had in his court the Nine Gems, his nine advisors, who were each known for a particular skill. One of these Gems was Birbal, known for his wit and wisdom. The story below is one of the examples of his wit. Do you have it in you to find the answer?
One day the Emperor Akbar stumbled on a small rock in the royal gardens and momentarily went off balance. He was in a bad mood that day and the incident only served to make him more angry. Finding a target for his mood of the day, he ordered the gardener's arrest and execution. Birbal heard of this and visited the gardener in the cell where he was being held awaiting execution. Birbal had known the gardener for many years and also knew of the gardener's immense respect and sense of loyalty for the king. He decided to help the gardener escape the death sentence and explained his plan to the gardener, who reluctantly agreed to go along.
The next day the gardener was asked what his last wish was before he was hanged, as was custom. The gardener requested an audience with the emperor. This wish was granted, but when the man neared the throne he tried to attack the emperor. The emperor was shocked and demanded an explanation. The gardener looked at Birbal, who stepped forward and explained why the gardener had attacked the emperor. The emperor immediately realised how unjust he had been and ordered the release of the gardener. How did Birbal manage this?
"Your Majesty," said Birbal, "there is probably no person more loyal to you than this unfortunate gardener. Fearing that people would say you hanged him for a silly reason and question your sense of justice, he went out of his way to give you a genuine reason for hanging him."
