Puzzling Adventures: Tales of Strategy, Logic, and Mathematical Skill

133 Pages·2005·1.98 MB·English

by  Dennis E. Shasha

DEDICATION
To my extended Family, loving, energetic, and confidently odd.
CONTENTS
Cover
Title Page
Dedication
Ecco: A Public Enigma
LOGIC
Shifty Witnesses
Terminating Leaks
Competitive Clairvoyance
Going South
The Color Fairies
Alternating Liars
Alpha Malos
Disposable Couriers
The Delphi Flip
Crowning the Minotaur
Safety in Difficulty
GRAPHS AND CIRCUITS
Fishy Business
Perfect Billiards
Ghost Choreography
Truck Stop
Trust No One
Pebbling a Polar Bear
The Graph of Life
Gridspeed
STRATEGY AND GAMES
Stacking the Deck
Analytical Linebacking
Venture Bets
Bluffhead
Adversarial Bifurcations
Ultimate Tic-Tac-Toe
Jump-Snatch
Short Taps
Grab It If You Can
Skychasers
Nanomunchers
Strategic Bullying
SCIENCE AND FORM
The Stone Tomb of Zimbabwe
Protein Chime
Lost Hiker
Noah’s Arc
Liquid Switchboard
Prime Squares
Repellanoids
COMBINATORICS
Safecracking
Hard to Surprise
Tanktops and Sunglasses
Rendezvous of the Stars
Solutions
Acknowledgments
About the Author
Copyright
Previous books by Dennis E. Shasha
ECCO: A PUBLIC ENIGMA
You’d think that if anyone knew Dr. Jacob Ecco well it would be me. We’ve
appeared in photographs together. We’ve taken trips together. We’ve even been
kidnapped together. But, in spite of the years I’ve known him, he continues to
baffle me.
The mystery begins with small eccentricities. He wears shorts year-round,
even when it’s bitter cold. He refuses to wear a tie, even at events in his honor.
He doesn’t drink alcohol or coffee, but seldom refuses a milk shake. He climbs
rocks, particularly enjoying overhangs ascending from the water, but avoids high
diving boards. Tycoons pay him large fees, but his lifestyle never changes and
checks lie uncashed in the mess of his desk.
Most detectives rely on observation, knowledge of human nature, and
varying amounts of muscle. Ecco relies only on deduction and mathematics. The
evidence for success would come from the calling cards of his clients—if he
bothered to keep them.
Every one of the cases in this book is accompanied by a small passage in
code. Ecco received each one on a postcard around the same time he
encountered each case. Ecco has only partly decoded these. The hints seem to
lead somewhere beyond the book.
The puzzles themselves came to Ecco in plain text. I present them to you in
exactly the form he heard them. When some parts of the cases remain unsolved,
you can try to solve them yourself, perhaps inventing new mathematics on the
way. This book is not for the faint of mind.
Understanding the puzzles, however, seldom requires formal training beyond
junior high school mathematics. Younger kids with sufficient imagination can
solve many of them. Even adults have a chance.
Reach, touch, then grasp.
New York City
Spring 2004
P.S. Many of the puzzles themselves have appeared in abridged form in the
“Puzzling Adventures” column of Scientific American. I expand them here to the
full versions that I have heard from Dr. Ecco, often including unsolved parts.
Ever the minimalist, Ecco has instructed me to remove all traces of his (or my or
even his niece Liane’s) presence from those puzzles. He has, however, allowed
the accounts previously seen in Dr. Dobb’s Journal to appear in full. Our little
trio has lately acquired Liane’s younger brother as a fledgling member, but those
adventures are still to come.
Logic
SHIFTY WITNESSES
“XBA’G NBARELGHhLGP iP QBE MPNBiTARGSP NSLTEiLA. c’i
fHFG GSP NSTPQ QTEP SjOELAG.”YEAPFGB
XE. YNNB iLj SLIP FHRRPFGTBAF QBE L JLhgTAR GBHE.WBiP
CEPCLEPO.
Skipping the preliminaries, the detective stated his problem: “We have five
witnesses whom we don’t trust. The five have trailed a group of 10 suspected
drug dealers. For each suspect, they take a vote about whether the suspect has
drugs. Here is a summary of the votes: Suspect 1: all five vote ‘has drugs.’
Suspect 2: all five vote ‘has no drugs.’
Suspect 3: three vote ‘has no drugs’ and two vote ‘has drugs.’
Suspect 4: all five vote ‘has drugs.’
Suspect 5: four vote ‘has drugs’ and one votes ‘has no drugs.’
Suspect 6: all five vote ‘has no drugs.’
Suspect 7: three vote ‘has drugs’ and two vote ‘has no drugs.’
Suspect 8: all five vote ‘has drugs.’
Suspect 9: all five vote ‘has no drugs.’
Suspect 10: four vote ‘has no drugs’ and one votes ‘has drugs.’
“Can you tell us which suspects have drugs given only that the total number of
lies among all witnesses is eight or nine and most of the lies claim ‘has no
drugs’ when the truth is ‘has drugs’? They are a corrupt bunch.”
WARM-UP.
What is the smallest number of lies there could be judging only from the
accusations?
SOLUTION to WARM-UP.
Every non-unanimous vote (disagreement) must correspond to a number of lies
at least equal to the minority view and perhaps the majority view. As we can see
there are four occasions of disagreement: three against two occurs twice and four
against one occurs twice. Adding up the minority views gives us six lies.