Book contents
- Frontmatter
- Contents
- Preface
- 1 “Dat Pussle”
- 2 Our Geometric Universe
- 3 Fearful Symmetry
- 4 It's Hip to Be a Square
- 5 Triangles and Friends
- 6 All Polygons Created Equal
- 7 First Steps
- 8 Step Right Up!
- 9 Watch Your Step!
- 10 Just Tessellating
- 11 Plain Out-Stripped
- 12 Strips Teased
- 13 Tessellations Completed
- 14 Maltese Crosses
- 15 Curves Ahead
- 16 Stardom
- 17 Farewell, My Lindgren
- 18 The New Breed
- 19 When Polygons Aren't Regular
- 20 On to Solids
- 21 Cubes Rationalized
- 22 Prisms Reformed
- 23 Cheated, Bamboozled, and Hornswoggled
- 24 Solutions to All Our Problems
- Afterword
- Bibliography
- Index of Dissections
- General Index
23 - Cheated, Bamboozled, and Hornswoggled
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- 1 “Dat Pussle”
- 2 Our Geometric Universe
- 3 Fearful Symmetry
- 4 It's Hip to Be a Square
- 5 Triangles and Friends
- 6 All Polygons Created Equal
- 7 First Steps
- 8 Step Right Up!
- 9 Watch Your Step!
- 10 Just Tessellating
- 11 Plain Out-Stripped
- 12 Strips Teased
- 13 Tessellations Completed
- 14 Maltese Crosses
- 15 Curves Ahead
- 16 Stardom
- 17 Farewell, My Lindgren
- 18 The New Breed
- 19 When Polygons Aren't Regular
- 20 On to Solids
- 21 Cubes Rationalized
- 22 Prisms Reformed
- 23 Cheated, Bamboozled, and Hornswoggled
- 24 Solutions to All Our Problems
- Afterword
- Bibliography
- Index of Dissections
- General Index
Summary
The smart alec rudely interrupts the speaker, ready to spoil the puzzle for everyone else. But he has got the puzzle wrong and does not know it. And he is squelched by a cool response. Thus did Sam Loyd frame the anecdote accompanying his mitre-to-square dissection puzzle. And Loyd delighted in quoting the Persian proverb “He who knows not, and knows not that he knows not, is a nuisance.”
But, ironically, it was Loyd, the audacious American who had tormented the world with the notorious 14–15 puzzle and his perplexing Get Off the Earth paradox, who had got it wrong. And it was the cool Englishman, Henry Dudeney, who took his pleasure in squelching Loyd's bogus 4-piece solution.
What was perhaps Sam Loyd's biggest goof occurred with the Smart Alec Puzzle. Loyd (Inquirer, 1901d) posed the puzzle, accompanied by a picture of a rude young man who interrupts the speaker to show off his knowledge. The attention-getting premise was that the smart aleck had assumed the puzzle to be the familiar one of cutting a mitre into four pieces of identical shape, whereas it was actually a new puzzle, that of dissecting a mitre into the fewest number of pieces that rearrange into a square. The artwork that accompanied the puzzle statement appears on the previous page. It has a charm that is irresistible.
Loyd's purported 4-piece solution, shown in Figure 23.1, was given in (Loyd, Inquirer, 1901e). And here the trouble begins, because Loyd's solution does not yield a square.
- Type
- Chapter
- Information
- DissectionsPlane and Fancy, pp. 268 - 277Publisher: Cambridge University PressPrint publication year: 1997