mathematics problems

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Product!

What is the product of the following expression?
(x - a)(x - b)(x - c)...(x - z) solution



The Broken Calculator

Amit's calculator has a ten digit display but only the last four digits are working. He enters a number more than four digits long and squares the number. To his surprise the display remains the same. What was the number? solution


Birthday Bet

How many people do I need in a room for it to be a good bet that at least two of them will have birthdays on the same day? Ignore leap years. solution


The Walled City

There is a walled city. When Anna stands on Ben's shoulders she can just see over the wall. When Ben stands on Ceri's shoulders he can see nothing but bricks. When Ceri stands on Deven's shoulders she can see over the wall easily.

Which pair would be taller than Ceri and Deven?

Is it possible to say who the tallest and shortest are? solution



Circles

The radii of the three circles shown are a, b and c, the largest being a and the smallest c. The straight line is a common tangent.
Find a relationship between a, b and c.
solution
The Edge of Cyberspace.

At the edge of cyberspace there is the hotel Aleph-Null. It is special because it has an infinite number of rooms. One day Idoru arrives with her infinite number of followers but to her dismay the hotel is completely full, with every room taken. "Not to worry" said the receptionist who was also a mathematician. "I can easily fit you all in, each with your own room, and whats more I won't have to ask anyone to leave." What did the receptionist do? solution
Radius

AB is length 8 and OB is length 5.

What is the radius of the circle? solution


Dividing His Flocks
A Classic Puzzle by Sam Loyd

A Western rancher, finding himself well advanced in years, called his boys together and told them that he wished to divide his herds between them while he yet lived.
"Now, John," he said to the eldest, "you may take as many cows as you think you could conveniently care for, and your wife Nancy may have one ninth of all the cows left." To the second son he said, "Sam, you may take the same number of cows that John took, plus one extra cow because John had the first pick. To your good wife, Sally, I will give one ninth of what will be left." To the third son he made a similar statement. he was to take one cow more than the second son, and his wife was to have one ninth of those left. The same applied to the other sons. Each took one cow more than his next oldest brother, and each son's wife took one ninth of the remainder. After the youngest son had taken his cows, there were none left for his wife. Then the rancher said: "Since horses are worth twice as much as cows, we will divide up my seven horses so that each family will own livestock of equal value." How many cows did the rancher own and how many sons did he have. solution

Poker

Given an ordinary deck of cards, what is the probability of drawing each kind of hand in poker? No discards, just the first five cards. Remember, aces can be high or low. solution

Prime Numbers

Prove that there are an infinite number of prime numbers. solution


Manhole Covers

Why are round manhole covers better than square manhole covers?



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