Puzzles

The SAT Problem That Everybody Got Wrong

Place two quarters flat on a table so that they are touching. Holding one coin stationary on the table, roll the other quarter around it, keeping edge contact between the two without slipping. When the moving quarter returns to its starting location, how many full rotations has it made? In other words, how many times has George Washington returned to his upright position in the graphic below?

Finding the heaviest ball within 2 weightings:

You have 8 balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more.

How can you find the ball that is heavier by using a balance and only two weightings?

Three Utilities Puzzle
A review of the history of the three utilities problem is given by Kullman (1979). He states that most published references to the problem characterize it as "very ancient". In the earliest publication found by Kullman, Henry Dudeney (1917) names it "water, gas, and electricity". However, Dudeney states that the problem is "as old as the hills...much older than electric lighting, or even gas". Dudeney also published the same puzzle previously, in The Strand Magazine in 1913.

Suppose there are three cottages and each needs to be connected to the gas, water, and electricity companies. Is there a way to make all nine connections without any of the lines crossing each other?

Einstein's Puzzle
The zebra puzzle is a well-known logic puzzle. Many versions of the puzzle exist, including a version published in Life International magazine on December 17, 1962. The March 25, 1963, issue of Life contained the solution and the names of several hundred solvers from around the world.

The puzzle is often called Einstein's Puzzle or Einstein's Riddle because it is said to have been invented by Albert Einstein as a boy; it is also sometimes attributed to Lewis Carroll. However, there is no known evidence for Einstein's or Carroll's authorship and the Life International version of the puzzle mentions brands of cigarette, such as Kools, that did not exist during Carroll's lifetime or Einstein's boyhood.

It is often claimed that only 2% of the population can solve the puzzle. The Zebra puzzle has been used as a benchmark in the evaluation of computer algorithms for solving constraint satisfaction problems.

There are five houses in five different colors in a row. In each house lives a person with a different nationality. The five owners drink a certain type of beverage, smoke a certain brand of cigar and keep a certain pet. No owners have the same pet, smoke the same brand of cigar, or drink the same beverage.

Other facts:
The Brit lives in the Red house.
The Swede keeps Dogs as pets.
The Dane drinks Tea.
The Green house is next to the White house, on the left.
The owner of the Green house drinks Coffee.
The person who smokes Pall Mall rears Birds.
The owner of the Yellow house smokes Dunhill.
The man living in the center house drinks Milk.
The Norwegian lives in the first house.
The man who smokes Blends lives next to the one who keeps Cats.
The man who keeps Horses lives next to the man who smokes Dunhill.
The man who smokes Blue Master drinks Beer.
The German smokes Prince.
The Norwegian lives next to the Blue house.
The man who smokes Blends has a neighbor who drinks Water.

The question is: who owns the fish?

Hint: Consider making a chart to help organize the information:

"The Insurance Man"

An insurance salesman knocks on the door of a home in a housing development. When a lady answers the door he asks, "How many children do you have?" She replies that she has three children. When he ask, "What are their ages?" she decides that he is being too noisy and refuses to tell him. He apologizes for his rudeness and asks for a hint about the children's ages. She says, "If you multiply their three ages together, you get 36." (Their ages are exact numbers). He thinks for a while and then asks for another hint. She then says, "The sum of their ages is the number on the house next door." He immediately jumps over the fence to determine this number. He once again returns to the lady for one more hint. "All right," she says, "the eldest plays the piano!" He then knows their ages. Do you?

"The Text Puzzle"

Study this paragraph and all things in it. What is vitally wrong with it? Actually, nothing in it is wrong, but you must admit that it is most unusual. Don't just zip through it quickly, but study it scrupulously. With luck you should spot what is so particular about it and all words found in it. Can you say what it is? Tax your brains and try again. Don't miss a word or a symbol. It isn't all that difficult.

"The Rabbit Puzzle"

A rabbit falls into a dry well, thirty meters deep. Since being at the bottom of a well was not her original plan, she decides to climb out. When she attempts to do so, she finds that after going up three meters, she slips back two. Frustrated, she stops where she is for that day and resumes her efforts the following morning with the same result. How many days does it take her to get out of the well?

"Reading Your Mind: Card Trick"

Try this a few times to see if it can read your mind.

"The Two Jar Puzzle"

Given a five-liter jar and a three-liter jar and an unlimited supply of water, how do you measure out four liters exactly?

Variation #1: With a nine-liter jar and a seven-liter jar, measure out exactly every measure from one to nine liters.

Variation #2: With a nine-liter jar and a six-liter jar, measure out exactly five liters.

"Twenty People at a Party Puzzle"

Suppose there are twenty people in a room. If Alice and Bob are any two of them, and Alice knows Bob, then you may assume that Bob knows Alice. Furthermore, if Alice does not know Bob then, likewise, Bob does not know Alice. Now, any individual among these twenty may know nobody else, or some but not all of the others, or know everybody in the room. However, what might surprise you is the fact that all twenty cannot each know a different number of people in the room. Put another way, there are at least two in the room who know exactly the same number of people. Can you reason out why this must be?

"Magic Squares"

Place the numbers 1 to 9 into the nine cells of a three-by-three square so that the sum of the entries along:

• each of the three rows total 15.

• each of the three columns total 15.

• and each of the two diagonals total 15.

The challenge is to find all eight solutions.

"2 Rectangles over 3 Rectangles Problem"

DIRECTIONS:

Draw two rectangles on top of three squares as show above. With one continuous line try to cross every segment on the diagram without going through the same line twice and the line cannot be broken. To make sure you see all the segments, I have marked them red in the figure below:

"The 100-Meter-Dash Puzzle"

If A, B and C run a 100-meter dash, each running at a uniform speed throughout, and if A beats B by 10 meter and B beats C by 10 meters, by how much does A beat C?

"Mathematical Symbol"

What mathematical symbol can be put between 5 and 9, to get a number bigger than 5 and smaller than 9?

"Mathematical Symbol"

The following equation is wrong: 101 - 102 = 1

Move one numeral to make it correct.

"Who can you trust?"

· Person A says "Person B is lying."

· Person B says "Person C is lying."

· Person C says "Person A and Person B is lying."

Who is telling the truth?

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