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MathProblem 84 12 pearls and a scale problem

In front of you are 12 pearls, 11 being real and one fake. The real ones all weigh the same and the fake one differs in weight from the real ones (may weigh more or less). With a balance scale and three weighings how can you weed out the fake one and dete

MathProblem 80 128 pennies and a blindfold problem

You are blindfolded before a table. On the table are a very large number of pennies. You are told 128 of the pennies are heads up and the rest are tails up. How can you create two subgroups of pennies, each with the same number of heads facing up? Solutio

MathProblem 79 Three humans, three monkeys, and a boat problem

One one side of a river are three humans, one big monkey, two small monkeys, and one boat. Each of the humans and the big monkey are strong enough to row the boat. The boat can fit one or two bodies (regardless of size). If at any time at either side of t

MathProblem 71 Nine pearls and a scale problem

You have nine pearls, eight are real and one is fake. All the real ones weigh the same and the fake weighs less than the real ones. Using a balance scale twice how can you weed out the fake one? Solution 8个真的，1个假的，且假的比真的轻。问怎么用两次把假的区分出

MathProblem 68 Four weights and a scale problem

Using a balance scale and four weights you must be able to balance any integer load from \(1\) to \(40\). How much should each of the four weights weigh? Solution 从数学角度来看，需要满足： \[a\cdot A+b\cdot B+c\cdot C+ d\cdot D=x, \ (1\leq x\leq 40) \]其

MathProblem 52 Two children problem

A woman is chosen at random among all women that have two children. She is asked do you have at least one boy, and she answers 'yes.' What is the probability her other child is a boy? Assume every pregnancy has a 50/50 chance to be a boy or a gi

MathProblem 51 Maximum volume of cone problem

You have a tortilla with radius 1 and wish to form a cone. You may cut out any wedge you like from the tortilla. The point of the wedge must be at the center of the circle. After cutting out the wedge you then attach the two straight edges remaining to fo

MathProblem 43 Wall and two houses problem

There is a castle surrounded by a circular wall. The wall has a north gate and a south gate. A yellow house lays 3 miles north of the north gate. A blue house lays 9 miles east of the south gate. What is the radius of the circle formed by the wall? Soluti

MathProblem 42 Drunken walk problem #1

A drunk is on one point of an n-gon, such that n is an even number. The drunk moves along the perimeter of the n-gon. Each steps takes him to an adjacent point, and every step is chosen at random. What is the expected number of steps before he arrives at

MathProblem 35 Light bulb problem #1

You have ten light bulbs. Five have an average life of 100 hours, and the other five have a average life of 200 hours. These light bulbs have a memoryless property in that their current age (measured in how long they have already been on) has no bearing o

MathProblem 34 Drug test problem

10% of the people in a certain population use an illegal drug. A drug test yields the correct result 90% of the time, whether the person uses drugs or not. A random person is forced to take the drug test and the result is positive. What is the probability

MathProblem 29 Four dogs and a square problem

Four dogs occupy the four corners of a square with side of length a. At the same time each dog starts walking at the same speed directly toward the dog on his left. Eventually all four dogs will converge at the center of the square. What path does each do

MathProblem 28 Furniture factory problem

A factory that produces tables and chairs is equipped with 10 saws, 6 lathes, and 18 sanding machines. It takes a chair 10 minutes on a saw, 5 minutes on a lathe, and 5 minutes of sanding to be completed. It takes a table 5 minutes on a saw, 5 minutes on

MathProblem 25 Guess the age problem

Person x and y have the following conversation: x: I forgot how old your three kids are. y: The product of their ages is 36. x: I still don't know their ages. y: The sum of their ages is the same as your house number. x: I still don't know their

MathProblem 17 Dartboard problem #1

A dart is thrown at a circular dart board of radius one. The dart can land at any place on the dartboard with equal probability. What is the mean distance between where the dart hits and the center of the board? Solution 一个半径为 \(1\) 的圆盘，向上面投掷飞镖，

MathProblem 23 Fork in the road problem

You are traveling down a path and come to a fork in the road. A sign lays fallen at the path indicating that one path leads to a village where everyone tells the truth and the other to a village where everyone tells lies. The sign has been knocked down so

MathProblem 85 Five pirates and a 1000 coins problem

Five pirates have come across a treasure of 1000 coins. According to pirate rules the pirate of highest rank must make a suggestion on how to divide the money. If a majority agree to his suggestion then it is to be followed by all the pirates. However, if

MathProblem 83 To confess or not confess problem

You and your partner in crime are both arrested and questioned separately. You are offered a chance to confess, in which you agree to testify against you partner, in exchange for all charges being dropped against you, unless he testifies against you also.

MathProblem 20 Nine minute egg problem

You are a cook in a remote area with no clocks or other way of keeping time other than a 4 minute hourglass and a 7 minute hourglass. You do have a stove however with water in a pot already boiling. Somebody asks you for a 9 minute egg, and you know this

MathProblem 16 Two coins problem

A box contains two coins. One coin is heads on both sides and the other is heads on one side and tails on the other. One coin is selected from the box at random and the face of one side is observed. If the face is heads what is the probability that the ot

MathProblem 14 Four pints of beer problem

A bartender has a \(3\) pint glass and a \(5\) pint glass. A customer walks in and orders \(4\) pints of beer. Without a measuring cup but with an unlimited supply of beer how does he get \(4\) pints in either glass? Solution 用 \(3\) 和 \(5\) 的