Dissections

Puzzles

• acute.trianglesCut a square into the fewest number of acute triangles. New
• cube.3.4.5.6Dissect a 6x6x6 cube into as few pieces as possible that can be reassembled into three cubes 3x3x3, 4x4x4... New
• cubed.cubeShow that a cube of integer side cannot be partitioned into a finite number of smaller cubes of integer sides, all of different sizes. New
• diskCan a disk be cut into similar pieces without point symmetry about the midpoint?
• hexagonDivide the hexagon into: 1) 3 identical rhombuses.
• iced.cakeA rectangular slice of cake ABED is iced along two sides, the icing being the L-shaped region BCGFDE, so... New
• isosceles.trianglesWhat is the fewest number of angularly unique isosceles triangles that can be pieced together to form a... New
• largest.circleWhat is the largest circle that can be assembled from two semicircles cut from a rectangle with edges a and b?
• pizza.cutsHow do you cut a round pizza into 8 pieces with 3 straight cuts? New
• planesWhat is the maximum number of parts into which 3-dimensional space can be divided by 5 planes? New
• rectangle.to.squareA rectangle with sides x and y is cut with straight cuts into pieces that are reassembled, by rotation and... New
• slice.cakeHow do you cut a rectangular cake in half that already has a rectangular piece removed? Added material
• square.70Since 1^2 + 2^2 + 3^2 + ...
• square.fiveCan you dissect a square into 5 parts of equal area with just a straight edge?
• squared.squareGiven a square of n X n proportion, break the square up into smaller squares none of which can be the same dimensions as another. New
• tesseractIf you suspend a cube by one corner and slice it in half with a horizontal plane through its centre of...
• vanishing.leprechaunHow does the "Vanishing Leprechaun" puzzle work, in which one leprechaun disappears or reappears when the... New
• wedding.cakeWith one straight cut, and only the knife as a tool, halve a slice of wedding cake iced on top and on one... New