The Discover Boggler
By Scott Kim
My puzzle column The Boggler appears every month in the popular science magazine Discover. Most of the puzzles are mathematical, and include at least three questions that start easy and get harder. On this page you will find the stories behind the puzzles, including questions not in the magazine, and letters from readers.

Discover. Read current and back issues, including the Bogglers.

Discussion board. Post your comments on the Bogglers.

Bogglers FAQ. Read about how I create the Bogglers.

Email me your comments and your corrections.



Nov 2002 — Numbers Racket
    Digit Dilemmas. Patterns in the digits of a digital clock.
    When One Plus One Doesn't Equal Two. A strange sort of addition.
    Cross Purposes. Weird fraction cancellation sometimes gets the right answer.
Oct 2002 — Hyperspace: Up, Out and Away
    Tesseract: Cube to the Fourth. Square is to cube as cube is to hypercube.
    4d Tictacktoe. Get three in a row in a 3 by 3 by 3 by 3 hypercube.
    HyperCross. Unfold the eight cubical faces of a hypercube.
Sep 2002 — Breaking Up is Hard to Do
    Divided Alphabet. Cut each letter into two congruent parts.
    Divided Words. Rearrange each pair of words into a pair of antonyms.
    Divided Roads. Color roads red or blue and avoid making triangles.
Aug 2002 — A Beautiful Equilibrium
    Based on the mathematics of John Nash, subject of the film and book A Beautiful Mind.
    He Who Goes First. Who wins in the game of Hex?
    The Nash Equilibrium. Two-player games can get stuck in nonoptimal strategies.
    Decisions, Decisions. Varieties of 2-player games.
Jul 2002 — Gardner of Mathematical Delights
    Tributes to mathematics journalist Martin Gardner.
    Rep-Tiles. Cut a shape into copies of itself.
    Lifeline. An introduction to Conway’s game of Life.
    Word Walk. Find names of topics that Gardner has written about over the years.
Jun 2002 — Ideal Proportions
    Based on the mathematical documentary Donald Duck in Mathmagic Land.
    Golden Rules. The golden rectangle, and friends.
    Tuning Up. The mathematics of musical harmony.
    Working the Angles. Find the best shots on a pool table.
May 2002 — Fermat’s Enigma
    Based on the book of the same name by Simon Singh, which chronicles Andrew Wiles history-making proof of Fermat’s Last Theorem.
    Pythagorean Cutup. Demonstrate the Pythagorean Theorem by cutting up shapes.
    Triples.. Find Pythagoream Triples — integers that satisfy a2+b2=c2.
    Counterexamples. Find counterexamples to variations of Fermat’s Last Theorem.
Apr 2002 — Mathematica Redux
    Based on the Mathematica exhibit designed by Charles and Ray Eames.
    Love Triangles. Find the pattern of triangles in space that cast particular shadows.
    Möbius Strip. What happens when you cut up a Möbius strip?
    Square Dance. Cut a rectangle into squares.
Mar 2002 — Remember Your SATs
    Numerous Analogies. xxx
    Be Glad These Weren't on your Text. xxx
    Letters are to Logic as ABC is to…? xxx
Feb 2002 — String Theory
    Knot a Problem. Walk around a building in a knotted path.
    Hanging Tough. Tricky ways to wrap a wire for hanging a picture.
    Hold that Line. Folding a loop of string into a polyhedron.
Jan 2002 — Welcome to the Fold
    Plain. Unforld the shape and get a letter.
    Wacky. Unfold the shapes and get an alphabet
    Origami. Fold the square and get a black and white letter.
Dec 2001 — Math Hits the Road
    Based on The Mathematical Explorer CD-ROM, by Stan Wagon.
    Roads Less Traveled. Match the wheel with the road
    Fractals on the Half Shell. Match the program with the design it generates.
Nov 2001 — Auto Mechanics
    Garage Shuffle. Park the cars and leave a path to each car door.
    Mileage Mystery. When does the odometer show all 10 digits?
    A-maze-ing Bumper Cars. Maneuver both remote control cars out of the maze.
Oct 2001 — It All Adds Up
    Row, Row, Row Your Square. Magic squares and new variations.
    Can You Digit? Find the digits that make the equation work.
    Factor Fiction. Factor powers of 10 so the factors have no zeroes.
Sep 2001 — H’ud Rns z Rdbqds
    All Codes Lead to Rome. Solve some simple cyphers.
    A Riddle Wrapped in a Mystery. A graphic cypher.
    Public Displays of Encryption. A complete explanation of public key encryption.
Aug 2001 — Circular Reasoning
    Variations on classic puzzles involving circles and spheres.
    Rolling Around. Roll one quarter around another.
    Round Trip. Walk in an equilateral right triangular path.
    Around the World. Tie a string around the equator.
Jul 2001 — Child’s Play
    Ship Shapes. Based on the game Battleship.
    Trick-Tac-Toe. Advanced variations of tic-tac-toe.
    Boxed In. Advanced strategy for the game of Dots and Boxes.
Jun 2001 — And the Winner Is...
    Electoral Confusion. Lose the vote and win the election.
    Flavor Face-Off. Paradoxes in different voting methods.
    Tennis Mismatch. Schedule a tennis tournament.
May 2001 — The King Was in His Countinghouse
    The Toothpick Tally. How many squares and triangles?
    Don’t Count that Dial! How many phone numbers are possible?
    Counting on your Fingers. How high can you count?
Apr 2001 — Tricks from the Flicks
    Harry Potter and the Boggling Bottles. Deduce the right bottle.
    A Pentomino Odyssey. Based on a game from the movie 2001.
    Mathematics Takes a Bow. Based on Good Will Hunting
May 2001 — The Language of Science
    Eye Hear You. Match the words to the sound waves.
    Ology-ology. What do these ologies study?
    Lost in Translation. Decypher poorly translate TV show titles.
Feb 2001 — A Bevy of Boxes
    No Matter How You Slice It. Slice a cube and what do you get?.
    Shape, Rattle and Roll. Find pairs that are the same 3d shape.
    Cubist Revival.Wrap a cube in a strip of paper. * Improved solution.
Jan 2001 — 2001: A Puzzle Odyssey
    Also Sprach Frank and Dave. Read their lips.
    Screen Play. Figure out how special effects were done.
    One Man's Monolith is Another Man's Tetrahedron.
Dec 2000 — Inventions
    Clip Joints. Identify advantages of paper clip designs.
    See My Point? Find mistakes in the drawing of a pencil.
    Accidental Inventions. Accidents that led to inventions.
Nov 2000 — Crossing Space-Time with Dr. Broth
    Puzzles by Michael Abrams and Jeffrey Winters, from their new book
Oct 2000 — 20/20 Visions
    20 Trees. Plant trees in X rows of Y trees.
    20 Questions. Deduce numbers from their divisors.
    20 Houses. Paint houses nonconsecutively.
Sep 2000
    Digital Dexterity. Tie your fingers in knots.
    Scrambled Geometry. Anagrams of geometry terms.
    Base Impulses. Write numbers in base -10 and beyond.
Aug 2000 — Folding
    Take Five. Fold pentominoes to make shapes.
    Crease is the Word. Fold a square to make many areas.
    Hoist the Colors. Fold a flag to bring colors together.
Jul 2000 — Four Sides to Every Problem
    Touchy Subject. Arrange squares of paper to touch.
    Queens at Peace. Arrange two groups of queens.
    Quadrilateral Thinking. Classify four-sided figures.
Jun 2000 — Iltoz
    Skydiving on Iltoz. Invent skydiving patterns.
    Constellations of Iltoz. Find letters in constellations.
    Satellites of Iltoz. Arrange satellites around a cube planet.
May 2000
    The Logician is In. Order the signs so all are true.
    Mixed-up Physicists. Anagrams on physicist names.
    Hidden Values. Deduce spreadsheet formulas.
Apr 2000
    Sum of the Above. Help Floobini read minds.
    Square Not. Arrange markers without making squares.
    A Perfect Match. Arrange matchsticks so area = perimeter.
Mar 2000
    Box Steps. Peel a cube to make a strip of squares.
    Détente. Arrange chess pieces so there are no attacks.
    Elementary Anagrams. Solve the alchemical equations.
Feb 2000 — Gödel, Escher, Bach
    Gödel. From Douglas Hofstader's Gödel Escher Bach.
    Escher. Make tessellation patterns out of letters.
    Bach. How many different scales are possible?
Jan 2000
    Rock Collecting. The classic Japanese Hiroimono game.
Dec 1999
    Cutting a Rug. Cut shapes into pieces and reassemble.
Nov 1999
    The Common Factor. Arrange numbers in a ring.
Oct 1999
    Change for the Better. Got change for a dollar?
Sep 1999
    Rogue Knights. Arrange chess knights in patterns.


Copyright 2000 Scott Kim.
All rights reserved.