Logicki problemi by Betty BellaItalia

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E rror processing SSI file Error processing SSI file Good evening! Welcome to Expand Your Mind! It's now about quarter past eight, and we're glad that you made a visit. This site is the only stop on the World Wide Web to blend logic, science, philosophy, and mythology, into a comprehensive mind expansion! Please read on... EYM encourages progressive thinking, the broadening of perspectives, and a refined understanding of the world around us. The relationship between solving perplexing puzzles, absorbing scientific knowledge, pondering philosophical questions, and debunking myths, will become apparent using logic as a vehicle. Expand Your Mind will challenge your intellect and offer fascinating applications to logical reasoning. "Logical" thinking extends well beyond solving puzzles and riddles; it fosters the exploration of situations rather than accepting the quick solution. Thrown away are the dead-end assumptions; uncovered are the hidden answers. Deductive reasoning, as will be illustrated, cultivates solution identification. Once you train your mind to expand and see past literal interpretations, the world around you will become much more intelligible. A prerequisite to going any further, however, is the mere will to expand your mind. Coupled with this desire, an eager embracing of abstract thought will produce fruitful results. For an overview of this site and its contents, please click on the graphic below to get started on your journey here at Expand Your Mind!

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WHY EXPAND YOUR MIND: When the Wright Brothers set out to build a flying contraption, many respected people thought the idea foolish. Everybody knew that a machine heavier than air could not fly. When Marconi tried to transmit a radio signal across the Atlantic, the experts ridiculed the idea of sending radio waves around the curved surface of the earth. When Galileo proposed that the earth rotated around the sun, and not vice versa, he was shamefully disbelieved. Yet each of these people changed the world by overcoming traditional thinking, and found ways to prove possible what was once thought not. These individuals were clearly evolutionary; they learned how to expand their minds. Neither the Wright Brothers, nor Marconi, nor Galileo, accepted the world for what it seemed; they strove to see past the illusion of the obvious. Before it was discovered that the earth was round, it was considered fact that the world was indeed flat. This instance alone, exemplifies that what we consider a truism today could be categorically disproved tomorrow. In this site, logic problems and puzzles will be used as a platform of logical understanding, followed by its application to science and an array of philosophical questions. Whether trying to stretch your mind to decipher provable logic problems, or contemplate some of the most inexplicable questions facing human kind (e.g. the origin of man, meaning of life, existence of a higher being, etc.), one must break free from conventional thought, for all of the answers lie within. Expanding your mind, in this context, is nothing more than merely thinking for yourself. To be free, one must think as an individual, and avoid the conforming forces of human nature.

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HOW TO EXPAND YOUR MIND: "Expanding your mind" is harder than it sounds. Solving the problems within this site and absorbing the depth of the philosophical questions pondered, will require such a widely open mind, it demands an entirely new method of thinking. One must reach a point of purity in thought, upon which, the most obvious and logical solutions will surface.

Descarte, a famous philosopher, once said, "If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things." Imagine how difficult is must have been for people living in the era of Columbus to accept that the world was indeed round. After thousands of years of roaming planet earth, it seemed implausible to humankind that the land was curved in shape. This flawed thinking came from a narrow perspective of basing conclusions solely on observations. So then, in order to expand your mind, one must get past trap-door assumptions, and accept the breadth of possibilities that exist. Sometimes truth hides behind the fallacies of the familiar answers. When solving some of these logic problems, a first reaction may be "it is impossible; there is not enough information." Although that is erroneous, thinking this will make it impossible, for you would be blinding yourself from the actual solution. This is the essence of logical problem solving... Believe there is an answer, believe you have the power to find truth, and allow yourself to think abstractly, and you will be on your way to expanding your mind.

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DEFINITION OF LOGIC: LOGIC \Log"ic\, n. 1. The science or art of exact reasoning, or of pure and formal thought, or of the laws according to which the processes of pure thinking should be conducted; the science of the formation and application of general notions; the science of generalization, judgment, classification, reasoning, and systematic arrangement; correct reasoning. Source: Webster's Revised Unabridged Dictionary

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HOW TO NAVIGATE THIS SITE: On the top left of each page, an easy-to-use interactive menu will be found in the red column. Any "Expand Your Mind" logos, when clicked, will take you to the home page. The pulldown menu labeled "Click to explore THIS PAGE" provides an index and direct access to the sections of the page that you are currently visiting. The second pulldown menu labeled "Click to explore ENTIRE SITE" is a complete index of the entire web site. Therefore, any page in this site can be accessed from any other page! All blue text, even when not underlined, are active links that will transport you to the corresponding section when clicked. If you have any problems or would like to offer suggestions on the navigation of this site, please visit our feedback page.

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CONTENT LISTING / DESCRIPTION: Logic Problems: Exercise your mind with three different styles of challenging problems. The puzzles vary from mathematical deduction, to spatial acuity, to

lateral thinking. They promise to expand your mind! Science and Facts: See the application of logic in action! The basis of science is exact reasoning. Different topics will be discussed including numbers, time, distance, speeds, among other fascinating facts and concepts. Philosophy: This section offers possibilities to some of the classic philosophical questions perplexing mankind. Wandering into this section of the site is for the open-minded, and those wishing to push logic to its furthest extreme. Myths Demystified: Myths and superstitions are debunked in this section with insightful and logical explanations. This area of the site, as with the philosophy section, may challenge your own beliefs. Proceed only with an open mind! Click "continue" below to test the expandability of your mind... (back to top)

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Exercise your mind with three different styles of challenging problems. The puzzles vary from mathematical deduction, to spatial acuity, to lateral thinking. They promise to expand your mind!

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INTRODUCTION TO LOGIC PROBLEMS: Logic Problems come in a variety of forms, and have been fascinating mankind for countless centuries. The three basic forms include classic logic problems, visual logic puzzles, and the newest and most difficult of the triad, lateral thinking.

The first two types require deductive reasoning and the application of multidimensional logic principles. Lateral thinking, on the contrary, requires "sideways" thinking in order to solve these tests of your creativity. Each type will be found on the following pages, separated into their respective sections outlined below. For a real challenge, check out the bonus section! As it would be unfair to provoke the mind with these problems without providing the answers, all solutions are given (except in the bonus section). In addition, two levels of hints are available for the lateral problems. The temptation to cheat will be great, as the answers are only a mouse click away. However, the solutions are intended for confirmation, not to settle curiosity. Rest assured, there are very logical and reasonable solutions to every problem herein, and the process of solving them on your own is the essence! Enjoy! So, let's get started. Choose one of the categories below:

These Classic Logic Problems are the easiest of the three types, and can be thought of as building blocks to some of the more difficult exercises. The use of simple math and logical deduction will provide the key to these clever problems. The solutions are provided, however, try only to use them to confirm your answers.

The Visual Logic Puzzles included in this section are accompanied by original artwork that are the basis of the puzzles. Various household items and a pencil and paper may be necessary to solve these tricky spatial puzzles. Some will require traditional logic, while others require "lateral thinking" (thinking outside of the box). Again, the solutions are provided to confirm your brilliance. Lateral Thinking requires the most abstract thought, and can be quite complex. Though the problems presented herein are relatively short in length, their solutions will take careful thought and the ability to see past the literal meaning of words and concepts. "Lateral thinking" is different from traditional linear thinking (where we progress sequentially from one step to the next). Thinking laterally requires the abandonment of ordinary reasoning, thereby eliminating inhibitions. In other words, rather than making assumptions to decipher explanations, think abstractly to reveal alternate (and the actual) solutions! In addition to the provided answers, you will find two levels of hints available to point you in the correct direction. Enjoy! How logical are you? If you can figure out the answer to this question, you will earn access to the bonus section of this site! Just click "Let me in!" below, enter the first word of the puzzle (lowercase) for the user name, and the solution to this puzzle as the password(entering digits only). Go ahead -- Expand Your Mind! Failed to execute CGI : Win32 Error Code = 123

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1. MILK JUGS: A milkman has two empty jugs: a three gallon jug and a five gallon jug. How can he measure exactly one gallon without wasting any milk? solution MILK JUGS:

The milkman filled the three gallon jug, and then emptied the contents into the five gallon jug. He then filled the three gallon jug again, and continued to fill the five gallon jug until it was full. The milk remaining in the three gallon jug was precisely one gallon.

SOCKS and SHOES: You are in the dark, and on the floor there are six shoes of three colors, and a heap of twenty-four socks, black and brown. How many socks and shoes must you take into the light to be certain that you have a matching pair of socks and a matching pair of shoes? solution Three socks and four shoes would guarantee that you would have a matching pair of each. Since there are only two colors of socks, it doesn't matter how many are in the heap, as long as you take at least three, you are certain to have two of the same. As for the shoes, you must pick four, because selecting only three could result in one shoe in each of the three colors!

3. PLAYING CARDS: There are three playing cards lying face up, side by side. A five is just to the right of a two. A five is just to the left of a two. A spade is just to the left of a club, and a spade is just to the right of a spade. What are the three cards? solution

4. TRUE STATEMENTS: A. The number of false statements here is one. B. The number of false statements here is two. C. The number of false statements here is three. D. The number of false statements here is four.

Which of the above statements is true?

solution

Option "C" is the answer: three statements are false. Since each statement concludes that there is a different number of false statements, that proves that only one statement can be correct (hence the object is to decide which statement is true). Given that one statement is true, by definition, the other three must be false!

5. FOUR DIGIT NUMBER: What is the four-digit number in which the first digit is one-third the second, the third is the sum of the first and second, and the last is three times the second? solution 1349 6. TRAINS: One train runs from A to B at 105 miles per hour, the other runs from B to A at 85 miles per hour. How far apart were the two trains 30 minutes prior to their crossing? solution They were 95 miles apart 30 minutes before the two trains crossed each other. Since one train is traveling at 105 MPH, and the other at 85 MPH, the relative speed is 190 MPH (105 + 85). One hour (or 60 minutes) before they crossed, they would have been 190 miles apart. Since the question asked how far away they were 30 minutes before they crossed, then it would be half that distance, or 95 miles.

7. MATH PUZZLE: Assume 9 is twice 5; how will you write 6 times 5 in the same system of notation?

solution

The answer is 27. Once you assume that 9 is twice 5, you conclude that 5 = 4.5 (9/2). Therefore, 6 times 4.5 is 27.

8. LOGIC POEM: The following verse spells out a word, letter by letter. "My first" refers to the word's first letter, and so on. What's the word that this verse describes? solution My first is in fish but not in snail My second in rabbit but not in tail My third in up but not down My fourth in tiara not in crown My fifth in tree you plainly see My whole a food for you and me FRUIT

9. TWIN BROTHERS: Suppose there are twin brothers; one which always tells the truth and one which always lies. What single yes/no question could you ask to either brother to figure out which one is which? solution

Answer: Would your brother say that you tell the truth? The key to this logic problem, is to find a question that the two brothers would answer differently, and that difference would therefore identify the two from each other. The lying brother would answer the above question "yes." The truthful brother would answer the same question "no."

10. THREE BOXES: There are three boxes, one contains only apples, one contains only oranges, and one contains both apples and oranges. The boxes have been incorrectly labeled such that no label identifies the actual contents of the box it labels. Opening just one box, and without looking in the box, you take out one piece of fruit. By looking at the fruit, how can you immediately label all of the boxes correctly. Which box did you open and how can you be sure to label all boxes correctly?

solution

The box that must be opened is the one labeled "apples and oranges." By definition, whichever fruit is inside, is the only fruit type that that box contains. Let's say that you found an apple in that box that was labeled with both apples and oranges; because you know it must therefore only contain apples, then you conclude that the box that is labeled "oranges" cannot contain only oranges, as all boxes have been said to be mislabeled. Thus, the box labeled "oranges" must contain both apples and oranges, leaving the box labeled "apples" to contain only oranges.

11. BOY or GIRL: A boy and a girl are sitting on the porch. "I'm a boy," says the child with black hair. "I'm a girl," says the child with red hair. If at least one of them is lying, who is which?

solution

The black-haired child is a girl, and the red-haired child is a boy. If at least one is lying, and there is one of each sex on the bench, then both must be lying. If only one was lying, then there would be two children of the same sex. Since the latter would not be following the given rules, then it is concluded that each child is of the opposite sex that they say they are.

12. FOOTBALL POSITIONS: Bill, Ken, and Mark are, not necessarily in this order, a quarterback, a receiver, and a kicker. The kicker, who is the shortest of the three, is a bachelor. Bill, who is Ken's father-in-law, is taller than the receiver. Who plays in which position? solution Since Bill is Ken's father-in-law, both Bill and Ken must be married. This leaves the only remaining person, Mark, to be the bachelor (and hence the kicker). Since Bill is taller than the receiver, Bill must not be the receiver. By process of elimination, we conclude that Bill is the quarterback. The remaining position (the receiver) goes to Ken. Therefore, Bill is the quarterback, Ken is the receiver, and Mark is the kicker. 13. THREE SPIES: Three spies, suspected as double agents, speak as follows when questioned: Albert: "Bertie is a mole." Bertie: "Cedric is a mole." Cedric: "Bertie is lying."

Assuming that moles lie, other agents tell the truth, and there is just one mole among the three, determine:

1.) Who is the mole? solution 2.) If, on the other hand there are two moles present, who are they? Solution: Bertie is the mole. Both Albert and Cedric are telling the truth. Hence, when Albert said, "Bertie is a mole," he was telling the truth, and giving you the correct answer. When Bertie said, "Cedric is a mole," he was lying, as he himself is a lying mole. When Cedric responded, "Bertie is lying," he was telling the truth, and also affirming that Bertie was lying. In the second case, if there were 2 moles, the identifications would be a direct inverse. Both Albert and Cedric would be moles, and Bertie would be telling the truth.

14. RIVER CROSSING: A man needs to cross a river in a canoe. With him, he has a bag of grain, a chicken, and a fox. He can only carry one of the three at a time. If he leaves the grain and the chicken, the

chicken will eat the grain. If he takes the grain, the fox will eat the chicken. How does he successfully cross the river with his load?

solution

The man first takes the chicken across, leaving it on the other side. He returns alone in the canoe and picks up the bag of grain. After bringing across the grain, he takes the chicken back to the original side, dropping him off, and picking up the fox. After bringing the fox to the other side, and leaving it with the grain, the man returns back to the original side, retrieving the chicken, and making his 3rd and final trip crossing the river. At no point was the fox left alone with the chicken, or the chicken with the grain.

15. 12 MARBLES: Given twelve marbles that are identical in size, shape, and color, determine which single marble is heavier in weight than the others. You are supplied with a balance and must conclude your determination in three weighings. solution

First, weigh all 12 marbles, 6 on each side of the scale (weighing #1). Whichever side is heavier, take those 6 marbles and weigh 3 on each side (weighing #2). Again, whichever side is heavier, take those 3 marbles, placing 1 to the side, and weighing the other 2, one on each side of the scale (weighing #3). During this weighing, if one marble weighs heavier than the other, the answer is obvious, and so too, if they balance perfectly, then the marble you put to the side is the heavier marble!

16. HOW OLD?: If you add the age of a man to the age of his wife, the result is 91. He is now twice as old as she was when he was as old as she is now. How old is the man and his wife? solution

The man is 52 and his wife is 39. The puzzle refers to the man as once being as old as the wife is "now." This gives you the first important piece of information; the man is older than the wife. Second, you know that the two ages will add up to 91. Third, you know that their difference in age is a constant variable. You can't, however, assume that they are close in age, but they must both be middle aged, otherwise it would be difficult to generate a number as high as 91 under the parameters of the problem. So, after gathering this information, and some guess and check work, you'd find that the man is now twice the age (52) of her age (26) when he was the age she is now (39).

17. CUT THE CAKE: How is it possible to cut a traditional circular cake into 8 equal size pieces, with only 3 cuts? solution

Make the first two cuts as cross-sections, making 4 equal pieces. The third and final cut is made horizontally through the middle, making a total of 8 pieces. 18. WHAT'S MY ADDRESS?: I live on Sunset Boulevard, where there are 6 houses on my side of the block. The house numbers are consecutive even numbers. The sum of all 6 house numbers is 8790. You don't know which block I live on, and it's a long street, but I will tell you that I live in the lowest number on my side of the block. What's my address? solution My address is 1460 Sunset Boulevard. First, you know that the house numbers are even and consecutive, so they must be approximately 1/6th the value of the sum (8790). In fact, the number that is 1/6th the total is the mean (average) for all 6 houses! This number, 1465 (8790 / 6), is how you come to the conclusion. There must be 3 house numbers greater than that number, and 3 house numbers less than that number, all being even and consecutive. Therefore, the 6 house numbers are 1460, 1462, 1464, 1466, 1468, 1470. The lowest house number, as per the question, is the answer: 1460.

19. PUZZLE SOLVING: If the puzzle you solved before you solved the puzzle you solved after you solved the puzzle you solved before you solved this one, was harder than the puzzle you solved after you solved the puzzle you solved before you solved this one, was the puzzle you solved before you solved this one harder than this one? solution Yes. There are only 2 puzzles being spoken of: this one, and the one before this one. The entire question could be rephrased like this: If the puzzle you solved before this one was harder than this one, was the puzzle you solved before this one harder than this one? Obviously, the answer to the question is simply yes.

20. BURNING ROPES: A rope burns non-uniformly for exactly one hour. How do you measure 45 minutes, given two such ropes? solution

First start burning rope 1 at both ends, and rope 2 at one end only. When rope 1 finishes burning (which will take 30 minutes), light the other end of rope 2. 45 minutes is up when rope 2 finishes burning.

21. PENNIES: Mary had a coin purse with fifty coins, totaling exactly $1.00. Unfortunately, while counting her change, she dropped one coin. What is the probability that it was a penny? solution There is an 85% probability that Mary dropped a penny. There are two (and only two) combinations of 50 coins that will add up to $1.00. These are: 40 Pennies, 2 Dimes, 8 Nickels, and 45 Pennies, 2 Dimes, 2 Nickels, 1 Quarter

With the first scenario alone, there would be a 80% probability, and the second scenario alone equates a 90% probability, respectfully. But because we don't know which she had, the probability is the average of the two, or 85%.

22. WHO DONE IT?: Melissa and Jessica were working on the computer along with their friends Sandy and Nicole. Suddenly, I heard a crash and then lots of shouts. I rushed in to find out what was going on, finding the computer monitor on the ground, surrounded with broken glass! Sandy and Jessica spoke almost at the same time: Jessica saying, "It wasn't me!" Sandy saying, "It was Nicole!" Melissa yelled, "No, it was Sandy!" With a pretty straight face Nicole said, "Sandy's a liar." Only one of them was telling the truth, so who knocked over the monitor?

solution

Nicole was telling the truth; Jessica broke the monitor. If only 1 of the 4 was telling the truth, that means that the other 3 were lying. By using deductive reasoning, one would conclude that the only possibility with the presented facts is that Jessica was lying when she said, "It wasn't me," Sandy was lying when she said, "It was Nicole," and Melissa also lied when she said, "No, it was Sandy." This leaves Nicole as the truth-teller, revealing Jessica as the culprit, having stated a direct lie when she said "It wasn't me!"

1. MILK JUGS:

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2. SOCKS and SHOES:

Three socks and four shoes would guarantee that you would have a matching pair of each. Since there are only two colors of socks, it doesn't matter how many are in the heap, as long as you take at least three, you are certain to have two of the same. As for the shoes, you must pick four, because selecting only three could result in one shoe in each of the three colors!

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3. PLAYING CARDS:

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4. TRUE STATEMENTS:

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5. FOUR DIGIT NUMBER:

1349

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TRAINS:

They were 95 miles apart 30 minutes before the two trains crossed each other. Since one train is traveling at 105 MPH, and the other at 85 MPH, the relative speed is 190 MPH (105 + 85). One hour (or 60 minutes) before they crossed, they would have been 190 miles apart. Since the question asked how far away they were 30 minutes before they crossed, then it would be half that distance, or 95 miles.

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6. MATH PUZZLE:

The answer is 27. Once you assume that 9 is twice 5, you conclude that 5 = 4.5 (9/2). Therefore, 6 times 4.5 is 27.

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7. LOGICPOEM:

FRUIT

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8. TWIN BROTHERS:

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9. THREE BOXES:

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BOY or GIRL:

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10. FOOTBALL POSITIONS:

Since Bill is Ken's father-in-law, both Bill and Ken must be married. This leaves the only remaining person, Mark, to be the bachelor (and hence the kicker). Since Bill is taller than the receiver, Bill must not be the receiver. By process of elimination, we conclude that Bill is the quarterback. The remaining position (the receiver) goes to Ken. Therefore, Bill is the quarterback, Ken is the receiver, and Mark is the kicker.

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Bertie is the mole. Both Albert and Cedric are telling the truth. Hence, when Albert said, "Bertie is a mole," he was telling the truth, and giving you the correct answer. When Bertie said, "Cedric is a mole," he was lying, as he himself is a lying mole. When Cedric responded, "Bertie is lying," he was telling the truth, and also affirming that Bertie was lying. In the second case, if there were 2 moles, the identifications would be a direct inverse. Both Albert and Cedric would be moles, and Bertie would be telling the truth.

RETURN TO PUZZLE RETURN TO LOGIC HOME PAGE RETURN TO HOME PAGE RIVER CROSSING:

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11. CUT THE CAKE:

Make the first two cuts as cross-sections, making 4 equal pieces. The third and final cut is made horizontally through the middle, making a total of 8 pieces.

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12. WHAT'S MY ADDRESS?:

My address is 1460 Sunset Boulevard. First, you know that the house numbers are even and consecutive, so they must be approximately 1/6th the value of the sum (8790). In fact, the number that is 1/6th the total is the mean (average) for all 6 houses! This number, 1465 (8790 / 6), is how you come to the conclusion. There must be 3 house numbers greater than that number, and 3 house numbers less than that number, all being even and consecutive. Therefore, the 6 house numbers are 1460, 1462, 1464, 1466, 1468, 1470. The lowest house number, as per the question, is the answer: 1460.

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13. PUZZLE SOLVING:

Yes. There are only 2 puzzles being spoken of: this one, and the one before this one. The entire question could be rephrased like this: If the puzzle you solved before this one was harder than this one, was the puzzle you solved before this one harder than this one? Obviously, the answer to the question is simply yes.

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14. BURNING ROPES:

First start burning rope 1 at both ends, and rope 2 at one end only. When rope 1 finishes burning (which will take 30 minutes), light the other end of rope 2. 45

minutes is up when rope 2 finishes burning.

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15. PENNIES:

There is an 85% probability that Mary dropped a penny. There are two (and only two) combinations of 50 coins that will add up to $1.00. These are: 40 Pennies, 2 Dimes, 8 Nickels, and 45 Pennies, 2 Dimes, 2 Nickels, 1 Quarter With the first scenario alone, there would be a 80% probability, and the second scenario alone equates a 90% probability, respectfully. But because we don't know which she had, the probability is the average of the two, or 85%.

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16. WHO DONE IT?:

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1. COINS: In three moves, rearrange the coins so that the three quarters are together and the two pennies are together with no empty space in between each coin. At the end of each move, the coins are always in a line as in the original configuration. Each move consists of moving two adjacent coins at one time. solution

2. CIRCLES: Using six contiguous straight lines, connect all of the sixteen circles shown below.

solution

3. TEAPOTS: If teapot A holds 32 ounces of tea, about how many ounces does teapot B hold? solution

4. MISSING SYMBOL: Complete the square logically. solution

5. TEN MATCHES: Remove six matches to make ten. solution

6. TRACING LINES: How is it possible to trace this design in one continuous movement without crossing a line on the way? solution

7. NINE NUMBERS: Place the numbers 1 through 9 in the circles below, such that each side of the triangle adds up to 17. solution

8. MOVING HOLE: By cutting this square piece of paper into two and only two pieces (and rearranging those pieces), how is it possible to move the hole into the center of the square? solution

9. CONNECT THE DOTS: How many squares can you create in this figure by connecting any 4 dots (the corners of a square must lie upon a grid dot). solution

10. TRIANGLES: How many triangles are located in the image below?

solution

11. GEARS: Gears A and D have 60 teeth each, gear B has 40 teeth, and gear C has 20 teeth. Suppose that gear B makes twenty complete turns every minute, explain the relative speed of gears A and D? solution

12. FOUR TRACKS: Four rollerbladers excercise around separate circular paths; each path is one third of a mile in length. They start simultaneously at the black spots, with speeds of six, nine, twelve, and fifteen miles per hour. By the end of the 20 minute workout, how many times will they have simultaneously returned to the spots where they started? solution

13. GOLFBALLS: Rearrange three golfballs so that the triangular pattern points down instead of up. solution

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