The Bear

A bear walks south for one kilometer, then it walks west for one kilometer, then it walks north for one kilometer and ends up at the same point from which it started. What color was the bear?

The Chicken and Egg Problem

A chicken farmer has figured out that a hen and a half can lay an egg and a half in a day and a half. How many hens does the farmer need to produce one dozen eggs in six days?

The Chicken and Leg Problem

A chicken farmer also has some cows for a total of 30 animals, and the animals have 74 legs in all. How many chickens does the farmer have?

The Bacteriologist

A scientist is experimenting with bacteria that are one micron in diameter and that reproduce by dividing every minute into two bacteria. At 12:00 PM, he puts a single organism in a container. At precisely 1:00 PM, the container is full.

At what time was the container half full?

How big was the container?

The Missing Dollar

Three students checked into a hotel and paid the clerk $30 for a room ($10 each). When the hotel manager returned, he noticed that the clerk had incorrectly charged $30 instead of $25 for the room. The manager told the clerk to return $5 to the students. The clerk, knowing that the students would not be able to divide $5 evenly, decided to keep $2 and to give them only $3.

The students were very happy because they paid only $27 for the room ($9 each). However, if they paid $27 and the clerk kept $2, that adds up to $29. What happened to the other Dollar?

Melanesia and Polynesia

Fiji (in Melanesia) and Samoa (in Polynesia) are two islands in the South Pacific Ocean. Fiji is about 970 kilometers (600 miles) west of Samoa. A small airplane can fly this distance in two hours.

When will you arrive in Fiji if you leave Samoa on a small airplane on Tuesday night at 11:30 PM?

I predict that your result will be 18

    Think of a number.

Add 7 to it.

Subtract 2.

Subtract your original number.

Multiply by 4.

Subtract 2.

The Bermuda Triangle and the Mysterious Square

The Bermuda Triangle is a place in the Atlantic Ocean where ships and airplanes supposedly disappear without a trace. In the picture below, a square disappears when we rearrange the pieces of the upper triangle to form the lower triangle. The pieces in both pictures are identical. Can you explain why the square is missing? You will need your knowledge of geometry to solve this problem.

The Wanderer

You start walking north and you walk in a straight line for two kilometers. When you look at the map, you discover that you actually walked one kilometer north and one kilometer south. How is this possible?

  The Cold Drink  

At a bar, there is a bucket containing ice, some of which has melted. A bartender gets an ice cube weighing 20 grams from the ice bucket and puts it into an insulated cup containing 100 grams of water at 20 degrees Celsius. Will the ice cube melt completely? What will be the final temperature of the water in the cup?

The Philatelist

My sister has six red stamps and three blue ones. In her collection, seven stamps are from Mexico and six stamps are from France. One stamp is purple and it is not from Mexico or France. Two of her Mexican stamps are red and one is blue. Two of her French stamps are blue and three are red. How many stamps does she have?

The Jewelry Box  

At an eBay auction, a woman's ring and a filigree jewelry box with a hand-painted ceramic top are on sale for $200.00 Dollars. The jewelry box is valued at $190.00 Dollars more than the ring. How much is the ring worth?

The Handshake  

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

Government Subsidy

The government pays farmers a specific fee for each row of four trees that they plant. An enterprising, but dishonest farmer found a way of planting five rows of four trees using only ten trees. How did he do it?

Eye Puzzle

This rectangle of seemingly random colored dots contains a message. Do you know the answer?

Numerology

Mathematical aptitude tests frequently have sets of numbers where you are supposed to figure out a pattern or guess the next number. For example,

(2, 4, 6, 8, 10)  is a list of even numbers corresponding to 2×n  for n=1, 2, 3, ...

(1, 1, 2, 3, 5)  is the well-known Fibonacci series where two adjacent numbers are added to produce the next number.

(1, 2, 3, 5, 7)  is a list of prime numbers.

(1, 2, 4, 8, 16)  is an exponential series corresponding to 2n  for n=0, 1, 2, ...

Can you figure out the special significance of the following sequence?   (2, 6, 10, 15, 19)

The Mathematics Class

All students in the physics class also study mathematics. Half of those who study literature also study mathematics. Half of the students in the mathematics class study physics. Thirty students study literature and twenty study physics. Nobody who studies literature studies physics. How many students in the mathematics class study neither physics nor literature?

The Pet Detective  

You have been promoted to pet detective while Ace Ventura guides some tourists on a safari. From the following clues, you must figure out who is the owner of each pet, and where the pet got lost.

1. A rabbit and a dog are two of the lost pets.

2. The pet lost in the garden is owned by Mary.

3. Robert does not own a dog.

4. John's pet was lost in the woods.

5. The cat was not lost in the woods or in the park.

The Wall Street Investor $ $ $

An investor trading through a discount stock broker that charges $10.00 Dollars per transaction bought 200 shares of Vola Tile Corporation at $50.00 Dollars per share. The stock quickly increased in value by 50%, but then lost 40% of its value. The investor sold the stock. How much money did the investor gain or lose?

  Boolean Enlightenment  

The path to enlightenment lies behind one of two doors. In front of each door stands a guard who knows which door leads to enlightenment, but one of the guards always lies and the other one always tells the truth. In your search for enlightenment, you are allowed to ask one guard only one question that can be answered "yes" or "no", but unfortunately, you do not know which guard is the liar. You will be banished to the dungeon of logical illiteracy if you fail in your quest. What question should you ask to find the path to enlightenment?

The Electrician

An electrician has two two-way switches, a light bulb, and a power source. How should he connect the terminals so that either switch can be used to turn the light on or off?

The Hematologist

After many years of looking through a microscope at human blood slides, a hematologist in a hospital laboratory is very excited that he found five different types of leukocytes (white blood cells) in a row. The hematologist gives you the following hints so that you can identify the white cells:

1. The lymphocyte is immediately to the right of the basophil. 2. The neutrophil is immediately to the left of the monocyte.

3. The eosinophil is not adjacent to the monocyte, the neutrophil, or the basophil.

Can you name the white cells from left to right?

The Thief in the Liar's Club  

A valuable painting was stolen from the Liar's Club, but the police are having a hard time identifying the culprit because every statement made by a member of the Liar's Club is false. Only four members visited the club on the day that the painting was stolen. This is what they told the police:

Ann: None of us took the painting. The painting was here when I left.

Bob: I arrived second. The painting was already gone.

Chuck: I was the third to arrive. The painting was here when I arrived.

Tom: Whoever stole the painting arrived before me. The painting was already gone.

Who of these four liars stole the painting?

The Odd Ball

There are twelve identical-looking balls, but one is either heavier or lighter than the other eleven. How can you determine which is the odd ball and find out whether this ball is heavier or lighter than the others using only three weighings with a balance?

The Fruit Vendor  

A fruit vendor bought 100 pounds of berries for $2.00 per pound and expected to double his investment by selling the berries for $4.00 per pound at an open-air market. The vendor only managed to sell 50 pounds of berries the first day and he sold the remainder on the second day. The fresh berries had a content of 99% water, but because of the hot weather, the berries dehydrated and contained only 98% water on the second day. How much profit did the vendor make?

Three Generations  

The grandson is about as many days old as the son is in weeks. The grandson is approximately as many months old as the father is in years. The ages of the grandson, the son, and the father add up to 120 years. What are their ages in years?

The Leaning Tower

Built from 1173 to 1350.Started leaning in 1178.

It is said that Galileo (1564-1642) dropped balls of various weights from the top of the Leaning Tower of Pisa to refute an Aristotelian belief that heavier objects fall faster than lighter objects. If the balls were dropped from a height of 54 meters, how long did it take for the balls to hit the ground?

How fast were the balls going when they hit the ground?

  Aquarius

You have to measure exactly 4 liters of water, but you only have a 3-liter bottle and a 5-liter bottle. How do you do it?

Ship in a Tub 

A toy ship is floating in a cylindrical container 10 centimeters in diameter that is partially filled with water. How much will the level of the water rise if a silver teddy bear weighing 100 grams is loaded on the ship? By the way, silver has a density of 10.49 g/cc.

If the teddy bear falls off the ship and sinks to the bottom of the container while the ship continues to float, how much will the level of the water rise compared to the original level with just the ship?

1. I visited my math teacher last February. My teacher told me there were 3 groups of students came to his house on that day already. He also told me each group had different numbers of students. He said it was a coincidence that the product of the numbers of students in each group was equal to the visiting date (today’s date). He asked me if I knew how many people came in each group

I looked at the calendar and found out that there might be 4 possible answers. So I asked my teacher a question. He replied: No. Then I gave him the correct answer. Do you know on what date I visited my teacher? How many people came in each group? What was the question I asked my teacher?

2. There were 2 tribes living on an island. The east tribal people always tell a lie. The west tribal people always tell the truth. Alan and Bryan came from the same tribe. However, we do not know which tribe they came from.

When they were asked the marital status, Alan said: “Both of us are married.” But Bryan said: “I am not married”. Are they really married?

3.

A very long integer, with 22 digits and trailing by the magic number 7, multiplied by 7 and made the result leading by 7, and shifted all other 21 digits to the right.

In the figure, the different letters might represent the same number. What is that long number?

4. A spider has 8 legs. A dragonfly has 6 legs and 2 pairs of wings. A cicada has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

5. Long time ago, a rancher spent $100.00 and bought 100 animals. There were 3 kind of animals he bought: each Bull cost him $10.00, each Cow cost him $5.00 and each Calf cost him $0.50. How many he bought for each kind of animal?

6. 5 Sailors and a monkey landed on an island in the southern Pacific Ocean. They found a big pile of coconuts. Since they were so tired and it was getting late, they all went to sleep instead.

Allan woke up at night. He wanted to get his share right then. He divided the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep.

Brad woke up (without knowing what had happened) after Allan. He divided the rest of the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep.

Charlie woke up (without knowing what had happened) after Brad. He divided the rest of the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep.

David woke up (without knowing what had happened) after Charlie. He divided the rest of the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep.

Earl woke up (without knowing what had happened) after David. He divided the rest of the coconuts evenly into 5 piles, but one coconut was left. He hid one pile for himself and gave the extra one to the monkey. He went back to sleep.

When they all awoke in the morning, they determined to divide the rest of the coconuts evenly into 5 piles. Each sailor got a pile. Again one coconut was left, and they gave it to the monkey. Everybody got one pile. How many coconuts did each person get?

7.As shown in the figure, each letter represents a distinct digit. What are A, B, C, and D?

8.