ABSTRACT
This chapter supplies solutions to the numbered puzzles throughout the book. The number of the solution coincides with the number of the puzzle. A different piano-hinging for a hexagon to two triangles. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution1_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_275" target-type="page">275</target>A 4-piece tube-cyclicly hinged T-pentomino to a V-pentomino. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution2_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Leaf-cyclic hinging of a trapezoid to a rectangle. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution5_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_276" target-type="page">276</target>Folding trapezoid with an uncooperative side to a rectangle. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution5_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> A 10-piece rounded piano-hinged rectangles when 2 < <italic>α</italic> < 3. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution6_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_277" target-type="page">277</target>7-Piece piano-hinged (<italic>l, w</italic>)-rectangle to a (3<italic>l, w</italic>/3)-rectangle. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution6_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Unhinged (11 × 14)-rectangle with 1 × 10 hole to a square. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution7_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Folding dissection of two similar rectangles to one. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution8_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_278" target-type="page">278</target>Folding dissection of small-roof house to a square. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution8_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Crossposition for three equal squares to one. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution8_3a.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_279" target-type="page">279</target>Folding dissection of three equal squares to one. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution8_3b.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Flat-cyclic-hinged dissection of three equal triangles to one. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution9_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_280" target-type="page">280</target>Folding dissection of triangles for <inline-formula> <alternatives> <mml:math display="inline" xmlns:mml="<a href="https://www.w3.org/1998/Math/MathML" target="_blank">https://www.w3.org/1998/Math/MathML</a>"> <mml:mrow> <mml:msup> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msqrt> <mml:mn>3</mml:mn> </mml:msqrt> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msqrt> <mml:mrow> <mml:mn>13</mml:mn> </mml:mrow> </mml:msqrt> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/eq204.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/eq204.tif</a>" xmlns:xlink="<a href="https://www.w3.org/1999/xlink" target="_blank">https://www.w3.org/1999/xlink</a>"/> </alternatives> </inline-formula> https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution9_2a.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Superposition and nets: triangles for <inline-formula> <alternatives> <mml:math display="inline" xmlns:mml="<a href="https://www.w3.org/1998/Math/MathML" target="_blank">https://www.w3.org/1998/Math/MathML</a>"> <mml:mrow> <mml:msup> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msqrt> <mml:mn>3</mml:mn> </mml:msqrt> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msqrt> <mml:mrow> <mml:mn>13</mml:mn> </mml:mrow> </mml:msqrt> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/eq205.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/eq205.tif</a>" xmlns:xlink="<a href="https://www.w3.org/1999/xlink" target="_blank">https://www.w3.org/1999/xlink</a>"/> </alternatives> </inline-formula> https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution9_2b.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_281" target-type="page">281</target>Tessellation-based five squares to two. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution10_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Flat-cyclic-hinged seven hexagons to one. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution10_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_282" target-type="page">282</target>Three of four distinct ways to form the P-pentomino. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution11_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Decomino dissection analogous to <italic>W</italic>-pentomino dissection. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution12_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_283" target-type="page">283</target>Piano-hinged dissection of squares for 2<sup>2</sup> + 4<sup>2</sup> + 5<sup>2</sup> + 6<sup>2</sup> = 9<sup>2</sup>. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution13_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Piano-hinged L-pentomino to a Greek Cross. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution15_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_284" target-type="page">284</target>Folding dissection of two hexagrams to a hexagon. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution16_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Different fold-hinging of an {8/3} to two octagons. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution16_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_285" target-type="page">285</target>Hinge-snug swing-hinged {12} to 1- and <inline-formula> <alternatives> <mml:math display="inline" xmlns:mml="<a href="https://www.w3.org/1998/Math/MathML" target="_blank">https://www.w3.org/1998/Math/MathML</a>"> <mml:mrow> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/eq206.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/eq206.tif</a>" xmlns:xlink="<a href="https://www.w3.org/1999/xlink" target="_blank">https://www.w3.org/1999/xlink</a>"/> </alternatives> </inline-formula>-squares. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution_m5_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> Piano-hinged three 2-triangles to a 1-hexagram. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution18_1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> <target id="page_286" target-type="page">286</target>Folding 1-hexagram and <inline-formula> <alternatives> <mml:math display="inline" xmlns:mml="<a href="https://www.w3.org/1998/Math/MathML" target="_blank">https://www.w3.org/1998/Math/MathML</a>"> <mml:mrow> <mml:mn>2</mml:mn> <mml:msqrt> <mml:mn>3</mml:mn> </mml:msqrt> </mml:mrow> </mml:math> <inline-graphic xlink:href="<a href="https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/eq207.tif" target="_blank">https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/eq207.tif</a>" xmlns:xlink="<a href="https://www.w3.org/1999/xlink" target="_blank">https://www.w3.org/1999/xlink</a>"/> </alternatives> </inline-formula>-triangle to a 2-hexagon. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429064722/a7356d02-dd90-4df1-bd03-2a741707fc4d/content/solution18_2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>
