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The Inquisitive Problem Solver is a collection of mathematical miniatures composed to stimulate and entertain. On a deeper level, these little puzzles, accessible to a general audience, provide a setting rich in mathematical themes. One of the larger purposes of the book is to show how everyday situations can lead an inquisitive problem solver to profound and far-reaching mathematical principles. Discussions accompanying the problems reinforce important techniques in discrete mathematics, and the solutions - which require verbal arguments - show that proofs and careful reasoning are at the core of doing mathematics. In addition, anyone reading this book will learn that asking good questions is just as important to the progress of mathematics as answering questions. The book contains more than a dozen open problems for further research by amateurs or professionals. This treasury of problems will serve as a resource for anyone seeking to improve their problem-solving knowledge and know-how.
| Preface | p. v |
| Bad calibration | |
| Getting inside a brick | |
| In the running | |
| The domino effect | |
| What a mesh! | |
| The sands of time | |
| Anyone for tennis? | |
| Tiresome parrot | |
| A wire cube | |
| A cube of many colors | |
| Paper folding | |
| Colored cubes | |
| No-one twice as rich | |
| Find the dud | |
| Eternal triangle | |
| Painting models | |
| Sums of consecutive numbers | |
| Hand in hand | |
| Unicursal | |
| Do-it-yourself | |
| Number the regions | |
| Fair proportion | |
| More or less | |
| Not much difference | |
| Leapfrog | |
| Slicing a cube | |
| Sums around a circle | |
| How many voted? | |
| Shelf space | |
| What's the difference? | |
| Shortest path | |
| Unneighborly circuit | |
| Emptying heaps | |
| The cookie monster | |
| Bull's-eye | |
| Off-off-off-price | |
| Sums and differences | |
| Fair shares | |
| Turning $0.88 into $1.60 | |
| Musical squares | |
| Pouring down | |
| Equal but different | |
| Mitosis | |
| Free-throw contest | |
| Restore these multiplications | |
| Seven-eleven | |
| All ten digits | |
| Minimize the walking | |
| Equally productive | |
| Join the dots | |
| Three truths, two lies | |
| Diminishing returns | |
| Fidgits with digits | |
| Plus or minus | |
| Truth or consequences | |
| Lying about lying | |
| Roads of destiny | |
| Twixt truth and falsehood | |
| Stringing along | |
| Magic square | |
| Count up and count down | |
| Seventh-fold deletion | |
| A binary cryptarithm | |
| First service | |
| Eight into six won't go | |
| Times are odd! | |
| Round-robin wrestling | |
| Knockout tennis | |
| Rummy | |
| Nine cubits | |
| Nine-fold insert | |
| Magic rectangle | |
| Dunrovian coinage | |
| An elevating experience | |
| Another elevating experience | |
| Squaring the triangle | |
| Plus-minus grid | |
| Staffing problem | |
| Difference of squares | |
| Making a soccer ball | |
| Clicker, the robot | |
| Tricolored triangles | |
| A game of Snap | |
| Variegated products | |
| Complete satisfaction | |
| Numberworm | |
| Longer worms | |
| Guideposts | |
| Straight strokes | |
| Heads I win, tails you lose | |
| Rewards for work well done | |
| The school dance | |
| Well-balanced neighbors | |
| A 9-hole and an 11-hole course | |
| Elephant waltz | |
| Equal sums | |
| Equal products | |
| Four-letter words | |
| Lost galoshes | |
| Six sums the same | |
| Collective bargaining | |
| A confusion of coins | |
| Completing the square | |
| Countdown | |
| Give or take | |
| Skipping around the track | |
| Fifty-fifty | |
| Casting out the threes | |
| Location, location, location | |
| Growth spurt | |
| Wheels within wheels | |
| Crossed polygons | |
| Turning points | |
| Two pointed questions | |
| Oddly even | |
| Latin squares with diverse diagonals | |
| Seeing double | |
| Empty nest | |
| Tetrominoes | |
| Intersecting lines | |
| Domino cover-up | |
| Secret lives | |
| Reverse ordering | |
| Different sums for different lines | |
| More diverse line sums | |
| A dollar a year | |
| The Sol LeWitt puzzle | |
| Leveling up | |
| Dial a pile | |
| Fencing a field | |
| Partitioned latin squares | |
| Balanced numbers | |
| Divisible digits | |
| Leg work | |
| Contending contestants | |
| Magic products | |
| Goggles retrieval | |
| Paper folding sequences | |
| Green acres | |
| Keeping in the nines | |
| Seven divisions | |
| Elementary, my dear Watson! | |
| Winners in, losers out | |
| Four square | |
| Less is more | |
| Take 'em away | |
| Trivalence | |
| Half and half | |
| Go for gold! | |
| Destructive Dan | |
| Let's face it | |
| Packing calissons | |
| Ballroom dance-cards | |
| Scrambled shoebox | |
| Covering with trominoes | |
| Four for four | |
| Tables for four | |
| Dot-to-dot | |
| Counterfeit coins | |
| Delegate mixer | |
| Round-robin volleyball | |
| Encoded pentomino tiling | |
| More pentomino rectification | |
| Beware of frost | |
| Tower of pizza | |
| Strange bedfellows | |
| Squaring the rectangle | |
| Some good ones | |
| Fair and square | |
| Try your luck | |
| Visitors from outer space | |
| Find the dominoes | |
| Find more dominoes | |
| Banquet seating | |
| A planned neighborhood | |
| A temperamental elevator | |
| Patternizing | |
| Minimal extraction | |
| Tom and Jerry | |
| Notched blocks | |
| Tiling with quadrilaterals | |
| Sum of digits of square | |
| Number of the beast | |
| Divisible digits | |
| Pretty products | |
| Meltdown | |
| A list of jousts | |
| Curious fences | |
| Cars or carts | |
| Chain reaction | |
| Two cryptarithms | |
| Odd neighbors | |
| The powers that be | |
| The towers that be | |
| Blacksmithery | |
| Crossnumber puzzle | |
| Happy campers | |
| A regular icosagon | |
| Parquet flooring | |
| Magic line | |
| Magic fifteen | |
| Tic-Tac-Toe | |
| All x-ed out | |
| Head on collision | |
| Staking claims | |
| One or both | |
| Help the king home | |
| Casting in the nines | |
| Operands and operants | |
| Toad Road | |
| Room for one more | |
| Tiling with trapdoor | |
| Lucky sevens | |
| Factorial digits | |
| Two sums the same | |
| The first shall be last | |
| Nonattacking queens | |
| Magic triangle | |
| Far flung points | |
| By air or sea | |
| Can you wing it? | |
| Outward bound | |
| Build more overpasses | |
| Point of no return | |
| A better plan | |
| Business card exchange | |
| Consecutive sums | |
| Incompetent advisors | |
| A number scale | |
| Give and take | |
| Chess tournament scores | |
| Equal and unequal shares | |
| Two more cryptarithms | |
| Peter makes his point | |
| Covering a disk | |
| Sentries in the square | |
| Forward thinking | |
| Tetromino tilings | |
| Divisibility by 11 | |
| Painting by numbers | |
| Gasp! Asp! | |
| Unlucky thirteen | |
| Animal sociology | |
| Musical chairs | |
| Taking the cake | |
| Domino tiling | |
| Divisors of repunits | |
| Modular triangles | |
| Digital sums | |
| More gold medalists | |
| House numbers in Straightsville | |
| No two in a line | |
| Lie detection | |
| Think of five numbers | |
| Dan's crazy computer | |
| The 13-coin problem | |
| The Treasury | p. 277 |
| About the Authors | p. 327 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
ISBN: 9780883858066
ISBN-10: 0883858061
Series: Maa Problem Books Series
Audience:
General
Format:
Paperback
Language:
English
Number Of Pages: 344
Published: 1st April 2002
Country of Publication: US
Dimensions (cm): 25.4 x 18.42
x 2.54
Weight (kg): 0.6
