CONTENTS        

 

          The page numbers were last updated on 6 Apr 2000.

 

INTRODUCTION     1

          Nature of This Work     1

          Similar Works     2

          Coverage     3

          Status of the Project     4

          Technical     6

          New Sections in This Edition     6

          Acknowledgements     6

 

CONTENTS     10

 

ABBREVIATIONS     18

          Diacritical Marks and Notation     18

          Abbreviations of Journals and Series      19

          Abbreviations of Publishers     19

          Abbreviations of Months     180

          Publishers' Locations     19

 

COMMON REFERENCES     20

 

SOME OTHER RECURRING REFERENCES     65

 

1.           BIOGRAPHICAL MATERIAL in Chronological Order     68

 

Alcuin, Fibonacci, Bachet, Leurechon/van Etten, Ozanam, Montucla, Carroll, Hoffmann, Loyd & Loyd Jr, Lucas, Schubert, Ball, Dudeney, Ahrens, Phillips.

 

2.           GENERAL PUZZLE COLLECTIONS AND SURVEYS     74

 

3.           GENERAL HISTORICAL AND BIBLIOGRAPHICAL MATERIAL     74

 

3.A.       General Historical Material     74

3.B.        Bibliographical Material     74

 

4.           MATHEMATICAL GAMES     80

 

4.A.       General Theory and Nim‑like Games     80

              4.A.1.        One Pile Game     80

              4.A.1.a.                The 31 Game     83

              4.A.2.        Symmetry Arguments     84

              4.A.3.        Kayles     84

              4.A.4.        Nim     85

              4.A.5.        General Theory     87

4.B.        Particular Games     88

              4.B.1.         Tic‑Tac‑Toe  =  Noughts and Crosses     89

              4.B.1.a.                In Higher Dimensions     96

              4.B.2.         Hex     97

              4.B.3.         Dots and Boxes     98

              4.B.4.         Sprouts     99

              4.B.5.         Ovid's Game and Nine Men's Morris     99

              4.B.6.         Phutball     105

              4.B.7.         Bridg‑It     105

              4.B.8.         Chomp     105

              4.B.9.         Snakes and Ladders     106

              4.B.10.       Mu Torere     108

              4.B.11.       Mastermind, etc.     108

              4.B.12.       Rithmomachia  =  The Philosophers' Game     108

              4.B.13.       Mancala Games     109

              4.B.14.       Dominoes, etc.     110.

 

5.           COMBINATORIAL RECREATIONS     111

 

5.A.       The 15 Puzzle, etc.     111

                  General     111

                  Early Alphabetic Versions     111

                  Loyd     111

                  The 15 Puzzle     112

              5.A.1.        Non‑square Pieces     118

              5.A.2.        Three Dimensional Versions     118

              5.A.3.        Rolling Piece Puzzles     119

              5.A.4.        Panex Puzzle     120

5.B.        Crossing Problems     120

              5.B.1.         Lowering from Tower Problem     127

5.C.       False Coins with a Balance     128

              5.C.1.        Ranking Coins with a Balance     130

5.D.       Measuring Problems     131

              5.D.1.        Jugs  &  Bottles     131

              5.D.2.        Ruler with Minimal Number of Marks     136

              5.D.3.        False Coins with a Weighing Scale     137

              5.D.4.        Timing with Hourglasses     137

              5.D.5.        Measure Half a Barrel     137

5.E.        Euler Circuits and Mazes     137

              5.E.1.         Mazes     141

              5.E.2.         Memory Wheels  =  Chain Codes     144

              5.E.2.a                 Pantactic Squares     145

5.F.        Hamiltonian Circuits     146

              5.F.1.         Knight's Tours and Paths     146

              5.F.2.         Other Hamiltonian Circuits     152

              5.F.3.         Knight's Tours in Higher Dimensions     153

              5.F.4.         Other Circuits In and On a Cube     153

5.G.       Connection Problems     154

              5.G.1.        Gas, Water and Electricity     154

5.H.       Coloured Squares and Cubes, etc.     154

              5.H.1.        Instant Insanity  =  The Tantalizer     154

              5.H.2.        MacMahon Pieces     155

              5.H.3.        Path Forming Puzzles     156

              5.H.4.        Other and General     157

5.I.         Latin Squares and Euler Squares     158

              5.I.1.          Eight Queens Problem     160

              5.I.2.          Colouring Chessboard with No Repeats in a Line     163

5.J.         Squared Squares, etc.     163

              5.J.1.          Mrs Perkins's Quilt     165

              5.J.2.          Cubing the Cube     166

              5.J.3.          Tiling a Square of Side  70  with Squares of Sides  1, 2, ..., 24     166

5.K.       Derangements     166

              5.K.1          Deranged Boxes of  A,  B  and  A & B     167

              5.K.2          Other Logic Puzzles Based on Derangements     167

              5.K.3          Cayley's Mousetrap     167

5.L.        Ménage Problem     167

5.M.       Six People at a Party  _  Ramsey Theory     168

5.N.       Jeep or Explorer's Problem     169

5.O.       Tait's Counter Puzzle:  BBBBWWWW  to  WBWBWBWB     170

5.P.        General Moving Piece Puzzles     172

              5.P.1.         Shunting Puzzles     172

              5.P.2.         Taquin     174

5.Q.       Number of Regions Determined by  N  Lines or Planes     17

              5.Q.1.        Number of Intersections Determined by  N  Lines     175

5.R.       Jumping Piece Games     175

              5.R.1.        Peg Solitaire     175

              5.R.1.a.                Triangular Version     178

              5.R.1.b.               Other shapes     179

              5.R.2.        Frogs and Toads:  BBB_WWW  to  WWW_BBB     179

              5.R.3.        Fore and Aft  _  3 by 3  Squares Meeting at a Corner     181

              5.R.4.        Reversing Frogs and Toads:  _12...n  to  _n...21     182

              5.R.5.        Fox and Geese, etc.     182

              5.R.6.        Octagram Puzzle     185

              5.R.7.        Passing Over Counters     185

5.S.        Chain Cutting and Rejoining     188

              5.S.1.         Using Chain Links to Pay for a Room     189

5.T.        Dividing a Cake Fairly     189

5.U.       Pigeonhole Recreations     190

5.V.       Think‑A‑Dot, etc.     191

5.W       Making Three Pieces of Toast     191

              5.W.1.       Boiling Eggs     192

5.X         Counting Figures in a Pattern     192

              5.X.1.        Counting Triangles     192

              5.X.2.        Counting Rectangles or Squares     194

              5.X.3.        Counting Hexagons     195

              5.X.4.        Counting Circles     195

5.Y.        Number of Routes in a Lattice     194

5.Z.        Chessboard Placing Problems     198

              5.Z.1.         Kings     198

              5.Z.2.         Queens     199

              5.Z.3.         Bishops     200

              5.Z.4.         Knights     200

              5.Z.5.         Rooks     201

              5.Z.6.         Mixtures     201

5.AA.     Card Shuffling     201

5.AB.     Folding a Strip of Stamps     1203

5.AC.     Properties of the Seven Bar Digital Display     203

5.AD.     Stacking a Deck to Produce a Special Effect     204

5.AE.     Reversing Cups     204

 

6.           GEOMETRIC RECREATIONS     205

 

6.A.       Pi     205

6.B.        Straight Line Linkages     206

6.C.       Curves of Constant Width     207

6.D.       Flexagons     208

6.E.        Flexatube     209

6.F.        Polyominoes, etc.     210

              6.F.1.         Other Chessboard Dissections     218

              6.F.2.         Covering Deleted Chessboard with Dominoes     220

              6.F.3.         Dissecting a Cross into  Zs  and  Ls     220

              6.F.4.         Quadrisecting an  L‑Tromino, etc.     221

              6.F.5.         Other Dissections into Polyominoes     223

6.G.       Soma Cube     224

              6.G.1.        Other Cube Dissections     224

              6.G.2.        Dissection of  63  into  33,  43  and  53,  etc.     225

              6.G.3.        Dissection of a Die into Nine  1 x 1 x 3     226

              6.G.4.        Use of Other Polyhedral Pieces     226

6.H.       Pick's Theorem     226

6.I.         Sylvester's Problem of Collinear Points     227

6.J.         Four Bugs and Other Pursuit Problems     227

6.K.       Dudeney's Square to Triangle Dissection     229

6.L.        Crossed Ladders     229

              6.L.1.         Ladder Over Box     231

6.M.       Spider & Fly Problems     231

6.N.       Dissection of a  1 x 1 x 2  Block to a Cube     232

6.O.       Passing a Cube Through an Equal or Smaller Cube  _  Prince Rupert's Problem     233

6.P.        Geometrical Vanishing     234

              6.P.1.         Paradoxical Dissections of the Chessboard Based on

                                          Fibonacci Numbers     234

              6.P.2.         Other Types     235

6.Q.       Knotting a Strip to Make a Regular Pentagon     237

6.R.       Geometric Fallacies     238

              6.R.1.        Every Triangle is Isosceles     238

              6.R.2.        A Right Angle is Obtuse     239

              6.R.3.        Lines Approaching but not Meeting     239

              6.R.4.        Others     239

6.S.        Tangrams, et al.     239

              General Histories     239

              Specific Items     240

              6.S.1.         Loculus of Archimedes     245

              6.S.2.         Other Sets of Pieces     246

6.T.        No Three in a Line Problem     247

6.U.       Tiling     248

              6.U.1.        Penrose Pieces     248

              6.U.2.        Packing Bricks in Boxes     248

6.V.       Silhouette and Viewing Puzzles     248

6.W.      Burr Puzzles     251

              6.W.1.       Three Piece Burr     251

              6.W.2.       Six Piece Burr  =  Chinese Cross     251

              6.W.3.       Three Piece Burr with Identical Pieces     253

              6.W.4.       Diagonal Six Piece Burr  =  Trick Star     253

              6.W.5.       Six Piece Burr with Identical Pieces     254

              6.W.6.       Altekruse Puzzle     254

              6.W.7.       Other Burrs     254

6.X.       Rotating Rings of Polyhedra     255

6.Y.        Rope Round the Earth     256

6.Z.        Langley's Adventitious Angles     257

6.AA.     Nets of Polyhedra     258

6.AB.     Self‑Rising Polyhedra     259

6.AC.     Conway's Life     259

6.AD.     Isoperimetric Problems     259

              6.AD.1.      Largest Parcel One Can Post     262

6.AE.     6"  Hole Through Sphere Leaves Constant Volume     261

6.AF.      What Colour Was The Bear?     262

6.AG.     Moving Around a Corner     264

6.AH.     Tethered Goat     265

6.AI.      Trick Joints     266

6.AJ.      Geometric Illusions     267

              6.AJ.1.       Two Pronged Trident     269

              6.AJ.2.       Tribar and Impossible Staircase     270

              6.AJ.3.       Café Wall Illusion     271

6.AK.     Polygonal Path Covering  N x N  Lattice of Points, Queen's Tours, etc.     271

6.AL.     Steiner‑Lehmus Theorem     273

6.AM.    Morley's Theorem     274

6.AN.     Volume of the Intersection of Two Cylinders     274

6.AO.    Configuration Problems     275

              6.AO.1.     Place Four Points Equidistantly  =  Make Four Triangles with Six

                                          Matchsticks     282

              6.AO.2.     Place an Even Number in Each Line     282

6.AP.     Dissections of a Tetrahedron     283

              6.AP.1.      Two Pieces     283

              6.AP.2.      Four Pieces     283

6.AQ.     Dissections of a Cross,  T  or  H   284

6.AR.     Quadrisected Square Puzzle    285

6.AS.      Dissection of Squares into a Square     285

              6.AS.1.       Twenty  1, 2, Ö5  Triangles Make a Square, i.e. Five Equal Squares to a

                                          Square     286

              6.AS.1.a.              Greek Cross to a Square     288

              6.AS.1.b.              Other Greek Cross Dissections     289

              6.AS.2.       Two (Adjacent) Squares to a Square     289

              6.AS.2.a.              Two Equal Squares to a Square     291

              6.AS.3.       Three Equal Squares to a Square     291

              6.AS.3.a.              Three Equal 'Squares' to a Hexagon     291

              6.AS.4.       Eight Equal Squares to a Square     292

              6.AS.5.       Rectangle to a Square or Other Rectangle     292

6.AT.     Polyhedra and Tessellations     293

              6.AT.1.      Regular Polyhedra     293

              6.AT.2.      Star and Stellated Polyhedra     294

              6.AT.3.      Archimedean Polyhedra     296

              6.AT.4.      Uniform Polyhedra     297

              6.AT.5.      Regular‑Faced Polyhedra     298

              6.AT.6.      Tessellations     298

              6.AT.6.a.              Tessellating with Congruent Figures     298

              6.AT.7.      Plaiting of Polyhedra     299

              6.AT.8.      Dürer's Octahedron     299

              6.AT.9.      Other Polyhedra   300

6.AU.     Three Rabbits, Dead Dogs and Trick Ponies     300

              China     301

              China/Paderborn     301

              Europe     302

              Modern Versions of the Three Rabbits Puzzle     305

              Dead Dogs   306

              Trick Ponies      308

6.AV.     Cutting Up in Fewest Cuts     308

6.AW.    Division into Congruent Pieces     308

              6.AW.1.     Mitre Puzzle     308

              6.AW.2.     Rep‑Tiles     309

              6.AW.3.     Dividing a Square into Congruent Parts     310

              6.AW.4.     Dividing an  L-Tromino into Congruent Parts     311

6.AX.     The Packer's Secret     311

6.AY.     Dissect  3A x 2B  to Make  2A x 3B,  etc.     311

              6.AY.1.      O'Beirne's Steps     313

              6.AY.2.      Swiss Flag Puzzle     314

6.AZ.     Ball Pyramid Puzzles     314

6.BA.     Cutting a Card so One Can Pass Through It     315

6.BB.      Doubling a Square Without Changing Its Height or Width     316

6.BC.     Hoffmann's Cube     316

6.BD.     Bridge a Moat with Planks     316

6.BE.      Reverse a Triangular Array of Ten Circles     317

6.BF.      Pythagorean Recreations     318

              6.BF.1.       The Broken Bamboo     318

              6.BF.2.       Sliding Spear  =  Leaning Reed     319

              6.BF.3.       Well Between Two Towers     321

              6.BF.4.       Rail Buckling     323

              6.BF.5.       Travelling on Sides of a Right Triangle     323

6.BG.     Quadrisect a Paper Square with One Cut     324

6.BH.     Moiré Patterns     324

6.BI.       Venn Diagrams for  n  Sets     325

6.BJ.       3D Dissection Puzzles     326

6.BK.     Superellipse     327

6.BL.      Tan-1 _ + Tan-1 ½  =  Tan-1 1,  etc.     327

6.BM.     Dissect Circle into Two Hollow Ovals     328

6.BN.     Round Peg in Square Hole or Vice Versa     329

6.BO.     Butterfly Problem     329

6.BP.      Early Matchstick Puzzles     329

6.BQ.     Covering a Disc with Discs     330

6.BR.     What is a General Triangle?     331

6.BS.      Form Six Coins into a Hexagon     331

6.BT.      Placing Objects in Contact     332

6.BU.     Construction of  n-gons     332

6.BV.     Geometric Constructions     334

 

7.           ARITHMETIC  &  NUMBER‑THEORETIC RECREATIONS     335

 

7.A.       Fibonacci Numbers     335

7.B.        Josephus or Survivor Problem     337

7.C.       Egyptian Fractions     349

7.D.       The First Digit Problem     350

7.E.        Monkey and Coconuts Problems     350

              7.E.1.         Versions with All Getting the Same     361

7.F.        Illegal Operations Giving Correct Result     363

7.G.       Inheritance Problems     363

              7.G.1.        Half + Third + Ninth, etc.     363

              7.G.2.        Posthumous Twins, etc.     368

7.H.       Division and Sharing Problems  _  Cistern Problems     370

              7.H.1.        With Growth  _  Newton's Cattle Problem     385

              7.H.2.        Division of Casks     386

              7.H.3.        Sharing Unequal Resources  _  Problem of the Pandects     388

              7.H.4.        Each Doubles Other's Money to Make All Equal, etc.     390

              7.H.5.        Sharing Cost of Stairs, etc.     392

              7.H.6.        Sharing a Grindstone     393

              7.H.7.        Digging Part of a Well     394

7.I.         Four Fours, etc.     396

              7.I.1.          Largest Number Using Four Ones, etc.     401

7.J.         Salary Puzzle     402

7.K.       Congruences     404

              7.K.1.        Casting Out Nines     404

7.L.        Geometric Progressions     406

              7.L.1.         1 + 7 + 49 + ...   &  St. Ives     408

              7.L.2.         1 + 2 + 4 + ....     409

              7.L.2.a.                Chessboard Problem     410

              7.L.2.b.                Horseshoe Nails Problem     413

              7.L.2.c.                Use of  1, 2, 4, ...  as Weights, etc.     414

              7.L.3.         1 + 3 + 9 + ...  and Other Systems of Weights     415

7.M.       Binary System and Binary Recreations     417

              7.M.1.        Chinese Rings     418

              7.M.2.        Tower of Hanoi     420

              7.M.2.a.               Tower of Hanoi with More Pegs     423

              7.M.3.        Gray Code     424

              7.M.4.        Binary Divination     424

              7.M.4.a.               Ternary Divination     426

              7.M.4.b.               Other Divinations Using Binary or Ternary     426

              7.M.5.        Loony Loop  =  Gordian Knot     428

              7.M.6.        Binary Button Games     429

7.N.       Magic Squares     431

              7.N.1.        Magic Cubes     442

              7.N.2.        Magic Triangles     445

              7.N.3.        Anti‑Magic Squares and Triangles     446

              7.N.4.        Magic Knight's Tour     447

              7.N.5.        Other Magic Shapes     448

7.O.       Magic Hexagon     450

              7.O.1         Other Magic Hexagons     451

7.P.        Diophantine Recreations     452

              7.P.1.         Hundred Fowls and Other Linear Problems     453

              7.P.2.         Chinese Remainder Theorem     467

              7.P.3.         Archimedes' Cattle Problem     472

              7.P.4.         Present of Gems     473

              7.P.5.         Selling Different Amounts 'At Same Prices' Yielding the Same     474

              7.P.6.         Conjunction of Planets, etc.     478

              7.P.7.         Robbing and Restoring     479

7.Q.       Blind Abbess and her Nuns  _  Rearrangement Along Sides of a  3 x 3  Square

                                Conserving Side Totals     481

              7.Q.1.        Rearrangement on a Cross     483

              7.Q.2.        Rearrange a Cross of Six to Make Two Lines of Four     484

7.R.       "If I Had One From You, I'd Have Twice You"     484

              7.R.1.        Men Find a Purse and 'Bloom' of Thymarides     489

              7.R.2.        "If I Had  1/3  of Your Money, I Could Buy the Horse"     494

              7.R.3.        Sisters and Brothers     501

              7.R.4.        "If I Sold Your Eggs at my Price, I'd Get ...."     501

7.S.        Dilution and Mixing Problems     501

              7.S.1.         Dishonest Butler Drinking Some and Replacing with Water     502

              7.S.2.         Water in Wine Versus Wine in Water     502

7.T.        Four Number Game     503

7.U.       Postage Stamp Problem     504

7.V.       xy  =  yx  and Iterated Exponentials     504

7.W.      Card Piling over a Cliff     505

7.X.       How Old is Ann? and Other Age Problems      506

7.Y.        Combining Amounts and Prices Incoherently     513

              7.Y.1.         Reversal of Averages Paradox     515

              7.Y.2.         Unfair Division     516

7.Z.        Missing Dollar and Other Erroneous Accounting     516

7.AA.     Negative Digits     517

              7.AA.1.      Negative Bases, etc.     517

7.AB.     Perfect Numbers, etc.     518

7.AC.     Cryptarithms, Alphametics and Skeleton Arithmetic     520

              7.AC.1.      Cryptarithms:  SEND + MORE  =  MONEY,  etc.     520

              7.AC.2.      Skeleton Arithmetic:  Solitary Seven, etc.     522

              7.AC.3.      Pan‑Digital Sums     523

              7.AC.4.      Pan‑Digital Products     525

              7.AC.5.      Pan‑Digital Fractions     527

              7.AC.6.      Other Pan‑Digital Expressions     527

              7.AC.7.      Self-descriptive Numbers, Pangrams, etc.     530

7.AD.     Selling, Buying and Selling Same Item     531

              7.AD.1.      Pawning Money     532

7.AE.     Use of Counterfeit Bill or Forged Cheque     532

7.AF.      Arithmetic Progressions     533

              7.AF.1.       Collecting Stones     534

              7.AF.2.       Clock Striking     536

7.AG.     2592     537

7.AH.     Multiplying by Reversing     537

              7.AH.1.      Other Reversal Problems     538

7.AI.      Impossible Exchange Rates     538

7.AJ.      Multiplying by Shifting     538

              7.AJ.1.       Multiplying by Appending Digits     540

7.AK.     Lazy Worker     540

7.AL.     If  A  is  B,  What is  C?     542

7.AM.    Crossnumber Puzzles     544

7.AN.     Three Odds Make an Even, etc.     545

7.AO.    Divination of a Permutation     547

7.AP.     Knowing Sum vs Knowing Product     550

7.AQ.     Numbers in Alphabetic Order     552

7.AR.     1089     552

7.AS.      Cigarette Butts     554

7.AT.     Bookworm's Distance     555

7.AU.     Number of Cuts to Make  n  Pieces     555

7.AV.     How Long to Strike Twelve?     556

7.AW.    28/7  =  13     556

7.AX.     Sum  =  Product,  etc.     557

7.AY.     Sum of Powers of Digits     557

7.AZ.     Divination of a Pair of Cards from its Rows     558

7.BA.     Cycle of Numbers with Each Closer to Ten than the Previous      560

7.BB.      Iterated Functions of Integers     560

7.BC.     Unusual Difficulty Making Change     561

 

8.           PROBABILITY RECREATIONS     562

 

8.A.       Buffon's Needle Problem     562

8.B.        Birthday Problem     562

8.C.       Probability that a Triangle is Acute     564

8.D.       Attempts to Modify Boy‑Girl Ratio     565

8.E.        St. Petersburg Paradox     565

8.F.        Problem of Points     565

8.G.       Probability that Three Lengths Form a Triangle     57

8.H.       Probability Paradoxes     567

              8.H.1.        Bertrand's Box Paradox     567

              8.H.2.        Bertrand's Chord Paradox     568

8.I.         Taking the Next Train     568

8.J.         Clock Patience or Solitaire     568

8.K.       Sucker Bets     569

8.L.        Nontransitive Games     569

 

9.           LOGICAL RECREATIONS     571

 

9.A.       All Cretans are Liars, etc.     571

9.B.        Smith _ Jones _ Robinson Problem     572

9.C.       Forty Unfaithful Wives     573

9.D.       Spots on Foreheads     573

9.E.        Strange Families     574

              9.E.1.         That Man's Father is My Father's Son, etc.     580

              9.E.2.         Identical Siblings who are not Twins     583

9.F.        The Unexpected Hanging     583

9.G.       Truthtellers and Liars     583

9.H.       Prisoner's Dilemma     585

9.I.         Hempel's Raven Paradox     585

9.J.         Use of a Fallen Signpost     585

9.K.       Carroll's Barber Paradox     585

 

10.         PHYSICAL RECREATIONS     587

 

10.A.      Overtaking and Meeting Problems     587

              10.A.1.       Circling an Army     598

              10.A.2.       Number of Buses Met     599

              10.A.3.       Times from Meeting to Finish Given     600

              10.A.4.       The Early Commuter     601

              10.A.5.       Head Start Problems     601

              10.A.6.       Double Crossing Problems     602

10.B.      Fly Between Trains     602

10.C.      Lewis Carroll's Monkey Problem     603

10.D.     Mirror Problems     604

              10.D.1.      Mirror Reversal Paradox     604

              10.D.2.      Other Mirror Problems     605

              10.D.3.      Magic Mirrors     605

10.E.      Wheel Paradoxes     606

              10.E.1.       Aristotle's Wheel Paradox     606

              10.E.2.       One Wheel Rolling Around Another     606

              10.E.3.       Hunter and Squirrel     607

10.F.      Floating Body Problems     607

10.G.     Motion in a Current or Wind     608

10.H.     Snail Climbing out of Well     610

10.I.       Limited Means of Transport  _  Two Men and a Bike, etc.     614

10.J.       Resistor Networks     614

10.K.      Problem of the Date Line     615

10.L.      Falling Down a Hole Through the Earth     617

10.M.     Celts  =  Rattlebacks     618

              10.M.1.      Tippee Tops     620

10.N.     Ship's Ladder in Rising Tide     620

10.O.     Erroneous Averaging of Velocities     620

10.P.      False Balance     621

10.Q.     Push a Bicycle Pedal     622

10.R.      Clock Hand Problems     622

10.S.      Walking in the Rain     624

10.T.      Centrifugal Puzzles     624

10.U.     Shortest Route Via a Wall     625

10.V.      Pick Up Puzzles  =  Pluck It     625

10.W.    Puzzle Vessels     625

10.X.      How Far Does a Phonograph Needle Travel?     629

10.Y.      Double Cone Rolls Uphill     629

10.Z.      The Wobbler     630

10.AA.   Non-Regular Dice    630

10.AB.    Bicycle Track Problems     632

10.AC.   Roberval's Balance     634

 

11.         TOPOLOGICAL RECREATIONS     635

 

11.A.      Scissors on String     635

11.B.      Two People Joined by Ropes at Wrists     636

11.C.      Two Balls on String Through Leather Hole and Strap  =  Cherries Puzzle     637

11.D.     Solomon's Seal     638

11.E.      Loyd's Pencil Puzzle     639

11.F.      The Imperial Scale     640

11.G.     Trick Purses     640

11.H.     Removing Waistcoat Without Removing Coat     641

              11.H.1.      Removing Loop from Arm     642

11.I.       Heart and Ball Puzzle and Other Loop Puzzles     642

11.J.       Möbius Strip     644

11.K.      Wire Puzzles     646

              11.K.1.       Ring and Spring Puzzle     647

              11.K.2.       String and Spring Puzzle     648

              11.K.3.       Magic Chain  =  Tumble Rings     648

              11.K.4.       Puzzle Rings     648

              11.K.5.       Ring Mazes     649

              11.K.6.       Interlocked Nails, Hooks, Horns, etc.     649

              11.K.7.       Horseshoes Puzzle     650

              11.K.8.       The Caught Heart     650

11.L.      Jacob's Ladder and Other Hinging Devices     650

11.M.     Puzzle Boxes     651

11.N.     Three Knives Make a Support     652

11.O.     Borromean Rings      654

11.P.      The Lonely Monk      654

11.Q.     Turning an Inner Tube Inside Out     655

11.R     String Figures     655

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