Index
To expand your mind you need to learn new facts and develop new modes of thinking that will make the information that you already know more useful. Solving the following problems requires a combination of world knowledge, mathematics, common sense, logic, and science (chemistry, physics). This is not an IQ test. There is no time limit.
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 ProblemA 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?
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?
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, she puts a single organism in a container. At precisely 1:00 PM, the container is full.
At what time was the container half full?
Leonardo Fibonacci was an Italian mathematician who lived during the Middle Ages (ca. 1170-1240). He is famous for the sequence consisting of the sum of the previous two numbers (1,1,2,3,5,8,13,...). Fibonacci influenced European commerce by introducing the principles of Indian and Arabian mathematics in his book Liber abaci (1202). Fibonacci posed the following problem in his book:
A man buys 30 live birds that include partridges, pigeons and sparrows for 30 dinars. A partridge costs 3 dinars, a pigeon costs 2 dinars, and two sparrows cost one dinar (i.e., each sparrow costs 1/2 dinar). How many birds of each kind did he buy?
A photographer wants to take a picture of a lighthouse with the full moon as background, but he wants the full moon and the lighthouse to be about the same size. The light house has a height of 22 meters, and the moon subtends an angle of about 0.53 degrees of arc to an observer on the Earth. How far from the lighthouse should the photographer place the camera to get the picture?
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?
Fiji (in Melanesia) and American Samoa (in Polynesia) are two islands in the South Pacific Ocean. Fiji is about 970 kilometers (600 miles) west of American Samoa. A small airplane can fly this distance in two hours.
When will you arrive in Fiji if you leave American Samoa on a small airplane on Tuesday night at 11:30 PM?
|
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 appears when we rearrange the pieces of the upper triangle to form the lower triangle. The pieces in both pictures are identical. Can you explain the origin of the square? You will need your knowledge of geometry to solve this problem.
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 Astronaut's PeeAn astronaut orbiting in a space capsule at normal atmospheric pressure ejects 100 grams of water into the vacuum of space. How much water will turn into ice?
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?
Find all equilateral triangles within the main triangle where the three vertices of each triangle have the same number or letter as illustrated in the example above. (Hint: There are more than five.)
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?
At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?
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?
This rectangle of seemingly random colored dots contains a message. Do you know the answer?
Mathematical aptitude tests frequently have sets of numbers where you are supposed to figure out a pattern or guess the next number. For example,
Can you figure out the special significance of the following sequence?
(2, 6, 10, 15, 19)
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?
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.
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 EnlightenmentThe 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?
An electrician has two two-way switches (single-pole, double-throw), 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?
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:
Can you name the white cells from left to right?
Hydrochloric acid is a corrosive, fuming, poisonous, highly acidic solution of hydrogen chloride (HCl). Sodium hydroxide is a caustic, strongly alkaline compound (NaOH) used in drain cleaners. If ingested, hydrochloric acid corrodes the mucous membranes, esophagus, and stomach causing dysphagia, nausea, circulatory failure and death. Sodium hydroxide, if ingested, will cause vomiting, prostration, and collapse. Why is it that if you mix these two substances in the right proportions before ingesting them you will not have any poisoning symptoms?
A valuable painting was stolen from the Liars' Club, but the police are having a hard time identifying the culprit because every statement made by a member of the Liars' Club is false. Only four members visited the club on the day that the painting was stolen. This is what they told the police:
Who of these four liars stole the painting?
At a farm, you are asked to identify these common plants from their blooms:
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?
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?
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?
AquariusYou 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?
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?
While shopping for groceries, you notice a new cooking oil product consisting of a blend of canola oil and olive oil. The label does not say in what proportions the oils are mixed, but the Nutrition Facts panel says that a 14 gram serving has 1 gram of saturated fat, 9 grams of monounsaturated fat, and 4 grams of polyunsaturated fat. What percentage of olive oil does the blend contain?
You probably eat this chemical every day. Do you know what it is?
You probably have heard of acronyms, superlatives, and pleonasms, but can you recognize one?
Take a quick on-line test to rate your knowledge of the English language.
New Orelans was founded in 1718, over 290 years ago. Hurricane Katrina brought flooding and devastation to New Orleans in 2005. The levees separating Lake Pontchartrain and Lake Borgne from New Orleans have been repaired, but the city remains at risk because many areas are at or below sea-level. Taking into consideration that global warming is melting the Arctic ice, how likely is it that New Orleans will still be inhabitable in the year 2100?
Sudoku puzzles provide an excellent outlet for people who are compulsive organizers. You don't have to sprain your back moving furniture or redecorating your home. All you have to do is arrange a 9 × 9 matrix so that every row, every column and every 3 × 3 non-overlapping matrix has the numbers 1 through 9. Sudoku is a fun game to play when you have some free time. The French newspaper La France introduced a number square puzzle very similar to the modern Sudoku at the end of the 19th century.
Some definitions:
Riddle - Anything that arouses curiosity or perplexes because it is unexplained, inexplicable,
or secret.
Puzzle - A game, toy, or problem, that requires ingenuity and often persistence in solving
or assembling.
Brain teaser - A form of puzzle that involves a lot of thinking (mental/cognitive activity).
Conundrum - A paradoxical, insoluble, or difficult problem; a dilemma.
Enigma - Ambiguous, inexplicable, or perplexing speech or text.
