Contemporary Brainteasers

Contemporary Brainteasers

by Terry Stickels
Contemporary Brainteasers

Contemporary Brainteasers

by Terry Stickels

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Overview

How many cards do I have to deal before I know for certain that you have a straight?
If two typists can type two pages in two minutes, how many typists will it take to type 18 pages?
How many days are in five million seconds?
If you think these are good questions, this is the book for you! Over two hundred entertaining puzzles involving mathematical and mechanical calculations include challenges to your lateral thinking and logical reasoning. When your brain's tired of being teased, you can consult the complete solutions.

Product Details

ISBN-13: 9780486818726
Publisher: Dover Publications
Publication date: 01/04/2017
Series: Dover Recreational Math
Sold by: Barnes & Noble
Format: eBook
Pages: 176
File size: 5 MB

About the Author

About The Author
Terry Stickels is the author of more than 25 puzzle books as well as two nationally syndicated columns: FRAMEGAMES, appearing in USA Weekend, and STICKELERS, a daily feature that appears in several papers, including The Washington Post, The Chicago Sun-Times, and The Seattle Post-Intelligencer.

Read an Excerpt

Contemporary Brainteasers


By Terry Stickels

Dover Publications, Inc.

Copyright © 2016 Terry Stickels
All rights reserved.
ISBN: 978-0-486-81872-6



CHAPTER 1

PUZZLES


1

If pulley D is rotating in the direction of the arrow, then pulley A

(a) is moving in the same direction

(b) is moving in the opposite direction

(c) will not be able to move at all.


2

How many cubes of any size are contained in this stack? All rows and columns run to completion unless you actually see them end.


3

A bucket filled with water weighs 25 lbs. When one-half of the water is poured out, the bucket and remaining water weigh 13.5 lbs. How much does the bucket weigh?


4

The three sides of a triangle have prime number lengths, w, x, and y, where 10<w<x<y<40. If x = 19, how many possible perimeters does this triangle have?

(a) 5

(b) 8

(c) 13

(d) 21

(e) infinite


5

With a normal deck of 52 playing cards, on what card dealt is the probability of getting a straight (five consecutive cards of any suit) 100%?

In other words, how many cards would I have to deal to you, face down, before you tell me to stop because you know, with 100% accuracy, you have a straight?


6

If it were three hours later it would be half as long until midnight as it would be if it were one hour earlier. What time is it now?


7

If 1/3 = 7 in some other system, then 5/16 is equal to what in that system?


8

Each figure contained within the largest square is also a square. What are the sizes of the squares with the question marks?


9

If the figure below is folded back into a cube, what side is opposite the blackened square?

What about opposite the transparent circle?


10

[MATHEMATICAL EXPRESSION OMITTED]

A solution for n is

(a) 4

(b) 9

(c) 64

(d) 128

(e) 256


11

Here is a coin puzzle that may appear to have a counterintuitive answer, but I assure you it is correct.

I flip a penny and a dime and hide the results from you but tell you "at least one of the coins came up heads."

What is the probability that both coins came up heads?


12

The letters A U V T Y have reflection symmetry across a vertical plane. The letters H I O X have both horizontal and vertical symmetry. What capital letters have reflection symmetry across the horizontal plane only?


13

If 10! (10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) were to be factored into prime numbers, how many 5 s would appear? What if the number were 15!, how many 5s then?


14

In the pulley system above:

(a) A has a mechanical advantage of 2 and B has a mechanical advantage of 3.

(b) A has a mechanical advantage of 3 and B has a mechanical advantage of 2.

(c) A has a mechanical advantage of 2 and B has a mechanical advantage of 4.

(d) Both systems have a mechanical advantage of 2.

(e) Both systems have a mechanical advantage of 3.


Which choice is the correct one?


15

In the picture, the weight of A is 20, the weight of B is 10, and the coefficient of friction f is .2

How heavy must Z be to keep A from sliding?


16

At a recent small gathering of friends, there were nine more women than men. If the ratio of women to men was 5 to 2, how many men and women were at the party?


17

I have a few objects I need to weigh with weights from 1 to 40 ounces. What are four weights I can use to be able to weigh any weight from 1 to 40 ounces (whole number weights only and including 1 and 40 ounces)? I'm trying to keep the number of weights I buy to a minimum, so what is the least number I would have to purchase of each of these four weights to accomplish my goal?


18

What number comes next? Remember, anything goes with sequence puzzles.

50 33 25 20 17 14 13 11


19

In the formula below, what is the value of g?

v = f × (1 - g)t


20

Given five points in space, connecting three points at a time to determine a plane (extending to infinity) what is the maximum number of lines that will result from all intersections?


21

Each figure contained within the largest square is also a square. What are the sizes of squares A, B, C, and D?


22

Tyler has a different style of eating candy. When he eats chocolates in the morning, he eats no other candy in the afternoon. If he eats chocolates in the afternoon, he has none in the morning.

In one period of time, he had no chocolate on 9 mornings and 6 afternoons, but there were 13 days when chocolate was eaten. How many total days were involved in that period?

Here are some tips that will help you solve this. There can be days when no chocolate is eaten, but any day counts when chocolate is eaten in the morning or afternoon, but not both.


23

The probability that any one person chose at random being born on a Friday is 1 in 7 or 14%. What is the probability that of seven people chosen at random, that one or more was born on a Friday? What is the probability that exactly one person was born on a Friday?


24

How many squares of any size can be found in the diagram below?


25

What number comes next in the following sequence?

0 4 -4 4 -12 4 -28 4


26

Imagine a square sheet of paper. Fold it diagonally to form a triangle, then fold it again diagonally. Snip off the three corners exactly the same size. Now open up the sheet.

Which shape will it look like?


27

Given three containers with capacities 12, 7, and 6 cups, the largest is full of water; the others are empty. Show how to measure nine cups of water into the first container by pouring water from one container to another. The usual rules apply: you can pour water from one container to another until either the first is empty or the second is full. You cannot just pour water onto the ground or add water from outside the system.


28

One of the following figures lacks a basic feature the other four figures have. Which figure is the odd one out?


29

Try this baseball math. The distance from home plate to the pitcher's mound is 60 feet, 6 inches. A 90 mph fastball will reach the plate in 0.458 seconds. If you moved back 90 feet from home plate, how fast would the ball have to travel to reach the plate in 0.458 seconds?


30

What numbers go in the last rectangle?


31

When the proper weights are assigned, this mobile is perfectly balanced. What are the three missing weights?


32

A group of college students took a summer job where they provided night security for a construction site. Five of the students had to be on duty every night, and the length of service for each student was to be 12 shifts only. The construction company needed security for 48 consecutive days. How many different students were needed?


33

The houses on a particular street are numbered 1, 2, 3, 4, 5, etc., up one side of the street, and then the numbers continue consecutively on the other side of the street back to the house opposite No. 1.

If house No. 12 is opposite house No. 35, how many houses total are on both sides of the street?


34

Look at the bounded areas 1 and 2. Which is larger? Are they equal? The four interior circles are equal.


35

We have two bags with two balls in each. One bag has two black balls, and the other has a black ball and a white ball. You randomly pick a bag and draw a ball, which is black.

What is the probability that the second ball you pick also will be black?


36

How many days are in 5,000,000 seconds?


37

Suppose you work at a nursery, and your boss wants you to plant rose bushes for a client.

The client wants the bushes in five rows with four in each row, in a way that is the most economically feasible.

What is the minimum number of rose bushes that will be needed to accomplish this?


38

[MATHEMATICAL EXPRESSION OMITTED]

(a) 81

(b) 1

(c) 3

(d) 16

(e) -9


39

A chemical company is transporting 1,000 pounds of a certain chemical by truck. The chemical is 95 percent water. Part of it will evaporate during the trip. By the end of the trip, the chemical is expected to be 90 percent water. How much will the remaining chemical weigh when it reaches its destination?


40

If two typists can type two pages in two minutes, how many typists will it take to type 18 pages?


41

Using four ls and no more than two math operations or symbols, what is the smallest positive number you can create? We'll give one answer, but there may be others. (For this puzzle, you can't use the factorial function (!) or trig functions.)


42

Quick takes:

1) 25/2 - 23/2 =

(a) 2 (b) 2π (c) 23/2 (d) 2-1

2)If the average of three numbers is w, and one of the numbers is q and another is p, what is the remaining number?

(a) w/q - 3 - p (b) 3q - p

(c) 3w - q - p (d) w - q - p/2

3)Evaluate (25/64)3/2.

(a) 25/128 (b) 52/82 (c) 125/512 (d) 2/3


43

Illustration 1 is a square piece of paper. Illustration 2 is the piece of paper folded in half, and Illustration 3 is the piece of paper folded into fourths with the corners snipped.

Imagine you have snipped off the four corners as shown in Illustration 3. Now open the piece of paper.

The result will look like:


44

Two water pumps working simultaneously at their respective constant rates took exactly 4 hours to fill a swimming pool.

If the constant rate of one pump was 1.5 times the rate of the other, how many hours would it have taken the faster pump to fill the pool if it had worked alone at its constant rate?


45

If two gallons of paint are needed to cover all sides of one cube, how many gallons are needed to cover all the exposed surfaces of the figure below? Assume the bottom of the figure is exposed. Hint: There are no hidden cubes.


46

What number comes next?

4 7 16 43 124 367


47

Below are 40 matchsticks. What is the minimum number of matchsticks that need to be removed so there is no square of any size remaining?


48

Two trains start from two different cities and travel toward each other at 60 mph and 50 mph respectively. At the time the trains meet, the first train has traveled 120 miles more than the second.

What was the distance between the two trains when they started?


49

A publisher is printing an article of 48,000 words. Two sizes of type will be used — one where a page consists of 900 words, and the other will have 1,500 words on a page. The article will be 40 pages long.

How many pages of each type will be used?


50

On the five dice below, one of the faces is incorrect and has the dots going in the wrong direction.

Which die has a face that is incorrect?


51

Below are four views of the same cube. If you were to unfold the cube, how would you fill in the diagram so that it shows the correct orientation of numbers and the letter E? We've given you a head start by placing the number 3.


52

4/5 of a pound of cheese is balanced perfectly by 1/5 of a block of the same cheese. What is the weight of the whole block of cheese?

(a) 2 pounds

(b) 4 pounds

(c) 5 pounds

(d) 10 pounds


53

How many triangles of any size are in the figure below?

(a) 3

(b) 5

(c) 8

(d) 11


54

A solid cube has 12 edges. If all 8 corners of a cube are sliced away, while leaving part of each edge intact, how many total edges are there?


55

In each pair shown below, which is the larger, or are they the same?

(a) [MATHEMATICAL EXPRESSION OMITTED]

(b) 318 or 99

(c) 223 + 223 or 224


56

232 + 1 is exactly divisible by a whole number. Which of the following numbers is exactly divisible by this same number?

(a) 216 + 1

(b) 216 - 1

(c) 7 × 223

(d) 296 + 1


57

On the face of a digital clock, like the one below, there are 28 line segments to represent the time - of course, not all are used at the same time. One of these segments is used more than any other one. Can you determine which one it is?


58

How many cubes are in the configuration below? All rows and columns run to completion unless you actually see them end.


59

A cube of 15 centimeters is painted on all of its sides. If it's sliced into 1-cubic-centimeter cubes, how many 1-cubic-centimeter cubes will have exactly one side painted?

(a) 125

(b) 528

(c) 1001

(d) 1014

(e) 1375


60

There are five Leeps in a Grat, seven Grats in a Bliz, and three Blizzes in a Zank. What is the number of Leeps in a Zank divided by the number of Grats in a Zank?


61

Nine identical sheets of paper are used to create the design below. If D was placed first and F placed seventh, in what order would G be placed?


62

What is x if

[MATHEMATICAL EXPRESSION OMITTED]


63

See if you can figure this one out.

100 students are majoring in math, business, or both. 72 percent of the students are business majors, and 58 percent are math majors.

How many students are majoring in both?


64

Below are three views of the same cube.

If you were to unfold the cube and lay it flat on a table, how would the remaining faces appear on the layout below?


65

Here's a fun puzzle you can do with pennies (or any coins for that matter). A total of 13 pennies are put into three piles, so that each pile has a different number of pennies.

What is the smallest number of pennies that could be in the largest pile?


66

A message was found in a strange code that read FLANG BRONO HASSI. It was determined that this meant WE COME IN PEACE. Then a message was found that read MANSO NASI FLANG, and this meant PEACE, LOVE, AND FREEDOM. Finally, BRONO BRANGO VANX was determined to mean IN THE LAST MINUTE. What does HASSI mean?


67

How can you create an answer of 64,000 by multiplying two numbers, neither of which contains a zero?


68

At a certain school, the ratio of boys to girls is 2 to 7. If eight more boys attend the school this year, the new ratio of boys to girls will be 1 to 3.

How many boys currently attend the school?


69

On a standard die, the opposite faces total 7. In our version, none of the opposite faces total 7. Below is our die from four different perspectives.

How many dots are on the side opposite the side with three dots?


70

Using 10, 20, 30, 40, 50, and 60 (50 is already given), can you assign the weights to make this mobile perfectly balanced on all levels? Each weight may be used once only.


71

Molly drives 42 miles to work. Due to construction, she can average only 10 mph on the first 21 miles of the trip.

How fast must Molly go on the second half of the trip to average 19 mph for the whole trip?


72

The number 258 + 1/5

(a) is an odd integer

(b) has a remainder of 2

(c) is an even integer

(d) has a remainder of 4


73

If today is Monday, and I told you I would meet you for dinner three days after two days before the day before tomorrow, when would I meet you?


74

Divide 50 into two parts so that the sum of their reciprocals is 1/12.

What are the two numbers?


75

The diagram shows three normal dice. How many dots are on the side of the last die that is facing the middle die?


76

One hundred dental specialists are attending a medical convention. Each specialist is either an orthodontist or an oral surgeon. At least one is an orthodontist. Given any two of the specialists, at least one is an oral surgeon.

How many are orthodontists and how many are oral surgeons?


77

There are two ls between 1 and 10 (inclusive) and 21 between 1 and 100 (inclusive). How many 1s are between 1 and 1,000,000 (inclusive)?


78

Bella is doing a lab experiment and just realized she has put a certain solution in the wrong cylindrical jar. She needs another cylindrical jar with a 30% larger diameter and the same volume as the jar she's currently using.

If the diameter of the new jar is increased by 30% without the volume changing, by what percent must the height be decreased? Remember, the volume of a cylinder is V = πR2 x h


79

What is the largest sum of money that cannot be reached using just two chips if one is valued at $10 and the other at $11?

Of course, you can use as many chips of each as you want.


80

What is the probability of rolling a six when a die is tossed twice?

(a) 1/2

(b) 1/36

(c) 1 1/36

(d) 1/12

(e) 7/36


81

Walking at 3/4 of her usual speed, Molly arrives at her destination 2 1/2 hours late.

What is her usual time for walking this distance?


82

The following puzzle features analytical reasoning. See if you can determine the relationships between the symbols and letter combinations to find solutions to the two unknowns.


(Continues...)

Excerpted from Contemporary Brainteasers by Terry Stickels. Copyright © 2016 Terry Stickels. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

Table of Contents

How many cards do I have to deal before I know for certain that you have a straight?
If two typists can type two pages in two minutes, how many typists will it take to type eighteen pages?
How many days are in five million seconds?
If you think these are good questions, this is the book for you! Over two hundred entertaining puzzles involving mathematical and mechanical calculations include challenges to your lateral thinking and logical reasoning. When your brain's tired of being teased, you can consult the complete solutions.
www.doverpublications.com

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