Suppose you have two five-card poker hands dealt from separate decks. You are told hand A contains at least one ace. You are told hand B contains the ace of spades. Which hand is more likely to contain at least one more ace? (answer), (solution).
Five pumpkins are weighed two at a time in all ten sets of two. The weights are recorded as 16, 18,19, 20, 21, 22, 23, 24, 26, and 27 pounds. All individual weights are also integers. How much does each pumpkin weigh? (answer).
A large tank has a steadily flowing intake and 10 outlet valves, the latter being all of the same size. With 10 outlets open, it takes two and one half hours to empty the tank; with 6 outlets open it takes five and one half hours to empty the tank. After the tank is empty and with all 10 outlets closed, how long will it take to fill the tank?
(answer),
(solution).
A courier pigeon departs Las Vegas for Reno at the same time as another courier pigeon departs Reno for Las Vegas. Both pigeons fly at constant speeds, although different from each other. They cross paths 2x miles from Las Vegas. After each arrives at their destination they immediately turn around, going back and forth without breaks. They cross paths the second time x miles from Reno. Where will they cross paths the third time?
(answer),
(solution).
You have a box of matches and six 64-minute fuses. Each fuse burns exactly 64 minutes but the rate of burning is inconsistent. A half a fuse would not necessarily burn in 32 minutes. The fuses are also not equally inconsistent. Two cut fuses of the same length would not necessarily burn in the same time. Without the use of a clock, scissors, or anything other than the matches and the fuses how can you create a 60-minute fuse?
(answer).
Fifty contestants for the Miss America pageant were arranged in ten rows and five columns on the Boardwalk in Atlantic City. One viewer of this display noticed that of the tallest women in each column that Miss Maryland was the shortest of the five. Another viewer noticed that of the shortest women in each row that Miss Nevada was the tallest of the ten. There are no ties, all fifty women have different heights. Who is taller, Miss Maryland or Miss Nevada?
(answer),
(solution).
The front wheels of a wagon measure 3.5 feet in diameter. The real wheels measure 4.25 feet in diameter. While the wagon is stopped somebody makes a chalk mark on both a front and rear wheel. How far must the wagon travel before both chalks marks return to their initial position at the same time?
(answer),
(solution).
5 cows can eat 2 acres of grass in 10 days. 7 cows can eat 3 acres of grass in 30 days. The grass grows at a constant rate and each cow eats at a constant rate. The length of the grass before the cows begin grazing is constant. How many days will it take 16 cows to eat 7 acres of grass?
(answer),
(solution).
A spider eats 3 flies a day. Until the spider fills his quota a fly has a 50% chance of survival if he attempts to pass the web. Assuming 5 flies have already made the attempt to pass, what is the probability that the 6th fly will survive the attempt?
(answer),
(solution).
I am as old as John will be when I am twice as old as John was when my age was half the sum of our present ages. John is as old as I was when John was half the age he will be 10 years from now. How old am I?
(answer),
(solution).
A, B, and C are three downs, each connected by a network of roads. There are 82 ways to get from A to B, including those routes that pass through C. There are 62 ways to get from B to C, including those routes that pass through A. The number of ways to get from A to C, including those ways passing through B, is less than 300. How many ways are there to get from A to C?
(answer),
(solution).
Two trains, A and B, leave their respective starting points at the same time and travel in opposite directions. They travel at constant speeds, and pass at point M. One travels at twice the speed of the other. If one of the trains leaves five minutes late they pass at a point 2 miles from point M. What is the speed of the slow train, in miles per hour?
(answer),
(solution).
Three playing cards, removed from an ordinary deck, lie face down in a horizontal row. Immediately to the right of the King there's a Queen or two. Immediately to the left of a Queen there's a Queen or two. Immediately to the left of a Heart there's a Spade or two. Immediately to the right of a Spade there's a Spade or two. Name the three cards in order.
(answer),
(solution).
The puzzleville dating service has m men and w women, such that m>w. Introductions are made by randomly drawing any two names (without replacement) out of the total membership. If one man and one woman is drawn then a blind date is arranged. The probability that a draw will result in one of each gender is exactly 50%. After an advertising campaign to attract women to the club 100 more members join the service. After the increase in membership both properties still hold true: m>w and a 50% probability of a successful drawing. After the increase how many men and how many women are in the service?
(answer),
(solution).
Five ants are on the corners of an equilateral pentagon with side of length 1. They each crawl directly towards the next ant, all at the same speed and traveling in the same orientation. How long will each ant travel before they all meet in the center? Hint: before attempting this problem please solve problem problem 29.
(answer),
(solution).
You are given $250 in promotional roulette chips. You may play roulette as long as you like but may only keep your winnings above the initial $250. You also may only play the even money bets like red and black. You also may only bet $10 at a time. With two zeros on the wheel the probability of winning any given bet is 18/38. What should your strategy be to maximize your expected winnings and what is the most you can expect to win?
(hint),
(answer),
(solution).
Three men and a boy are gathered in your orchard to pick apples. The boy can shake the apples off the trees as fast as the men can pick them up. Any one of the men can shake apples off the trees 25% faster than the other two men and boy can pick them up. The same number of apples are gathered regardless of who is the shaker, as long as everybody is always doing something and no excess apples are left on the ground. (Note: anybody can divide their time between shaking and gathering.) How should you divide $500 between the 3 men and the boy, according to their contribution to the team effort?
(answer),
(solution).
You pick three different numbers from 0 to 9. What is the probability that a dollar bill chosen at random will contain all 3 of your numbers in the serial number? Note: the serial number has 8 digits, you may assume that an equal number of each combination is in circulation.
(answer),
(solution).
A drag racer accelerates at a uniform rate from its starting point. It travels the last one fourth of the distance from the starting point to the finish line in 3 seconds. How long did it take to travel the entire distance from starting point to finish line?
(answer),
(solution).
You are trapped in a small phone booth shaped room. In the middle of each side of the room there is a hole. In each hole there is a light switch. You can't see in the holes but you can reach your hands in them and flip the switches. You may stick your hands in any two holes at the same time and flip none, either, or both of the switches as you please. Nothing will happen until you remove both hands from the holes. You succeed if you get all the switches into the same position, after which time you will immediately be released from the room. Unless you escape, after removing your hands the room will spin around, disorienting you so you can't tell which side is which. How can you escape? The fewest possible turns that I know if is five.
(solution).