Clock
What is the angle between the minute hand and the hour hand at 3:15 on an analog clock? No, its not 0.
The Rope Bridge
Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it's only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?
The oldest play the piano
Two MIT math grads bump into each other while shopping at Fry's. They haven't seen each other in over 20 years.
First grad to the second: "How have you been?"
Second: "Great! I got married and I have three daughters now."
First: "Really? How old are they?"
Second: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..."
First: "Right, ok... Oh wait... Hmm, I still don't know."
Second: "Oh sorry, the oldest one just started to play the piano."
First: "Wonderful! My oldest is the same age!"
How old was are the three daughters?
100 doors in a row
You have 100 doors in a row that are all initially closed. you make 100 passes by the doors starting with the first door every time. the first time through you visit every door and toggle the door (if the door is closed, you open it, if its open, you close it). the second time you only visit every 2nd door (door #2, #4, #6). the third time, every 3rd door (door #3, #6, #9), etc, until you only visit the 100th door.
What state are the doors in after the last pass? which are open which are closed?
Paths count
Given a 5x7 grid , A is a point on the top-left corner and B a point on the bottom-right corner. The only moves allowed are to the right and the bottom.
How many paths exists from A to B?
5 pirates
Five pirates have 100 gold coins. they have to divide up the loot. in order of seniority (suppose pirate 5 is most senior, pirate 1 is least senior), the most senior pirate proposes a distribution of the loot. they vote and if at least 50% accept the proposal, the loot is divided as proposed. otherwise the most senior pirate is executed, and they start over again with the next senior pirate. what solution does the most senior pirate propose? assume they are very intelligent and extremely greedy (and that they would prefer not to die).
Add all the natural numbers below one thousand that are multiples of 3 or 5.
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.
Find the sum of all the even-valued terms in the Fibonacci sequence which do not exceed four million.
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ... Find the sum of all the even-valued terms in the sequence which do not exceed four million.
Find the largest prime factor of a composite number.
The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ?
Find the largest palindrome made from the product of two 3-digit numbers.
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99. Find the largest palindrome made from the product of two 3-digit numbers.
What is the smallest number divisible by each of the numbers 1 to 20?
2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest number that is evenly divisible by all of the numbers from 1 to 20?
Chameleons
At one point, a remote island's population of chameleons was divided as follows:
* 13 red chameleons
* 15 green chameleons
* 17 blue chameleons
Each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.).
Is it ever possible for all chameleons to become the same color? why or why not?
Find the 10001st prime.
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6^(th) prime is 13. What is the 10001^(st) prime number?
Trailing zeros
Factorial 5 is 1x2x3x4x5 = 120, which has 1 trailing zero.
How many trailing zero for factorial 100 ?