102 Math Brainteasers for High School Students : Arithmetic, Algebra and Geometry Brain Teasers, Puzzles, Games and Problems with Solution , livre ebook

Tom eMusic - Krzysztof Ciesielski ,
traduit par Ben Torrent , Adam Fisher

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75 pages

English

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102 Math Brainteasers (Grades 10–12) is a subtle selection of arithmetic, algebra, and geometry problems, which efficiently train the mind in math skills. It will be a helpful and stimulating tool for students attending higher-level science or engineering programs as well as high school students preparing themselves for Mathematical Olympiads or math competitions; similarly, math teachers will naturally recognize its benefits. The problems can equally be used in classrooms or as an extracurricular activity. The book contains a range of problems: Some are relatively simple, while others can be qualified as intermediate or difficult.
It is the author’s sincere hope that solving the problems may bring intellectual pleasure not only to high school but also to university students. The fun and games are truly delightful, original, and solving them is even more enjoyable thanks to their lively illustrations.

Informations

Publié par	Tom eMusic
Date de parution	08 septembre 2021
Nombre de lectures	10
EAN13	9781623213244
Langue	English
Poids de l'ouvrage	1 Mo

Informations légales : prix de location à la page 0,0374€. Cette information est donnée uniquement à titre indicatif conformément à la législation en vigueur.

Extrait

Illustrations and cover
Jacek Skrzydlewski
English Translation and Adaptation
Adam Fisher
Benjamin Torrent
Typesetter
PanDawer
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher.
© Copyright by Tom eMusic
ISBN 978-1-62321-324-4
www.tomemusic.com
New York 2021
TABLE OF CONTENTS

FOREWORD
INSTRUCTIONS
PROBLEMS
HINTS AND ANSWERS – PART ONE
HINTS AND ANSWERS – PART TWO
HINTS AND ANSWERS – PART THREE
HINTS AND ANSWERS – PART FOUR
FOOTNOTES Okładka Title Page Copyright Page TABLE OF CONTENTS FOREWORD INSTRUCTIONS PROBLEMS HINTS AND ANSWERS – PART ONE HINTS AND ANSWERS – PART TWO HINTS AND ANSWERS – PART THREE HINTS AND ANSWERS – PART FOUR FOOTNOTES
FOREWORD
The math problems proposed in this book differ significantly in terms of substance and difficulty. They have, however, one thing in common: Their intellectual appeal makes them worth sharing with others! Solving each of the problems requires a non-standard approach and an alert mind for pitfalls (or traps for ho-ho’s ) 1 are many. While virtually all the proposed brainteasers are grounded in elementary mathematics, some require a better knowledge of a certain subject or another.
In writing this brainteaser collection one of my governing intentions was to cast the net far and wide so as to interest the widest possible readership. Some sets of problems, in my opinion, can be successfully given to eager grade school pupils, while some other problems may turn out to be tall orders even for professional mathematicians or veterans of the International Mathematical Olympiads. The book is organized in such a way that the simplest problems are usually found at the beginning and the most difficult ones at the end. It’s not a hard and fast rule, though. First of all, the degree of difficulty in the case of mathematical problems is not always immediately obvious as one man’s ceiling is another man’s floor, and sometimes a problem found at the end of the book will be solved in a matter of minutes with very simple methods, while earlier problems may have proved to be daunting.
Solutions are included in the book, but in a non-standard fashion — as described in the INSTRUCTIONS section found on the following page. I strongly recommend reading them before proceeding onwards. It is my sincere wish that this book may provide all inquisitive minds with novel math problems to enjoy.
Krzysztof Ciesielski
INSTRUCTIONS
One of the most beautiful things about mathematics is problem solving, and one of the most rewarding moments in the life of a true mathematician is when s/he succeeds in solving something requiring a lot of intellectual effort. I would be very pleased if my readers looked upon this book of math contest problems as a gauntlet thrown down that they do not hesitate to pick up. This book is meant as a selection of tasks to puzzle over, never giving up even though some of them might prove a pretty tough nut to crack.
It may occasionally happen that you reach the brink of giving up, and instead of trying harder, you flip through several pages to find the answer, thus missing out on what might have been a peak experience. But sometimes all you need is just a hint and the earlier enthusiasm returns. That is why the problems proper are followed by hints and clues to put you on the right track.
I did not limit myself to giving just one hint or dividing the answer into two parts. In order to encourage the readers to face the challenge, I decided to present the answers in a somewhat fragmentary form. More often than not when having read the info available in the chapter ‘Hints and Answers — Part One’, you move on to ‘Part Two’ only to find a follow-up in the form of further hints, but seldom with a complete reasoning. To find the latter, you will need to visit ‘Part Three’ and on numerous occasions also ‘Part Four’. The place where all the info on a given problem comes to an end is marked with the sign ‘THE END’. If it happens to appear, for example, in ‘Part Two’, you will find no further hints on that issue in the third and fourth parts. If, on the other hand, explanations are not followed by the sign in question, that means that the subsequent part provides further help. It can happen that certain details will be left for the reader to fill in.
My sole and sincere intention was to discourage readers from looking at the answers too quickly. That is why ‘Part Four’ never contains a complete answer, and you need to read from ‘Part One’ all the way to the ‘THE END’ sign. I fully realize that it can prove somewhat awkward at times, but the first and foremost intention should be to solve the problems. I also advise against looking at the very end of the book, because nowhere is it said that you will find the essence of the answer there.
The number of parts (1, 2, 3, and 4) does not depend on the degree of difficulty of a given problem. The answers are divided into parts irrespective of the complexity of the problems.
Finally, one more important thing. Sometimes when checking the answer to a problem we can — more accidentally than on purpose — cast an eye at a neighboring solution, which can lessen the satisfaction derived from solving the problem unassisted. That is why the drawings in the answers are less precise than they otherwise could be. Moreover, on a few occasions some words in the answers are given in code. The code is simple and involves shifting back the letters in the English alphabet by one, and accordingly, b → a , d → c , l → k , and — watch out here — a → z . Thus, for example, the word Mathematics would be coded as Lzsgdlzshbr .
PROBLEMS
Problem 1
Color envelopes are packed by the hundred in cardboard boxes. It takes the stationer’s five seconds to bring down a box from the shelf. Removal of one envelope from the box takes one second (no matter whether he pulls the envelopes out one by one or counts them out in the box and takes out the required quantity). The stationer can deal with envelopes of one color only at a time and can’t possibly take down boxes with, for example, green and blue envelopes, simultaneously. A customer has asked for 10 green, 10 blue and 60 yellow envelopes. How long will the shop owner take (at his fastest) to hand the customer the envelopes he asked for?

Problem 2
A snail climbs up a tree trunk. Every day it covers a distance of 18 feet, but each night it slides down 12 feet. The height of the tree is 30 feet. After how many days will the snail reach the treetop?

Problem 3
A cyclist had covered the distance from A to Z at a speed of 30 mph. Upon reaching his destination, he instantly turned back and cycled all the way back at 20 mph. What was his average speed at which he covered the AZA route?
Problem 4
In the bottom drawer, there are 4 black and 4 blue socks. They’ve been dropped there just any old how. What’s the smallest number of socks that must be taken out to be sure of having one correctly matched pair?
Problem 5
Into a Norroway restaurant, famous for its plain but delicious cuisine, came a distinguished patron with two friends of his. He ordered three large potato pancakes prepared according to an old recipe.
“One for each of us,” he said. “Each of the pancakes must be fried in two minutes: one minute per side. We are in a tearing hurry, and I would appreciate having the pancakes ready in 3 minutes! Chop-chop! Make it snappy!”
Unfortunately there were only two frying pans free at the moment. Either of them could hold just one pancake. Frying two pancakes at the same time and then the third would have meant a minute-delay. Was there a way to serve the pancakes just as they had been ordered?

Problem 6
What is the last digit of the following number?

Problem 7
How many positive solutions does the equation have?
Problem 8
I have a very precise double-pan balance with a set of weights. I also have ten bulging sackfuls of coins. The point is that one of them contains counterfeit coins. A genuine coin weighs 10 grams, whereas a fake one only 9 grams. Can you help me find which sack contains exclusively fake coins by means of only one weighing?

Problem 9
In a soccer cup 379 teams participate. The matches are played on successive Saturdays. This is a knock-out tournament, and each tie is, of course, followed by a penalty shoot-out. If in any round the number of teams is odd, then, each time, a randomly selected team will automatically qualify for the next round; the choice of the team will be decided by a draw performed by the cup’s sponsor. How many games have to be played before the final winner is declared?

Problem 10
We have six line segments at our disposal. Their respective lengths are: 1, 2, 3, 2018, 2019, 2020. How many different triangles can we build out of them?
Problem 11
You are given three so-called ‘hour-strings’, each of which burns completely