Divide these shapes to achieve the requested goals

Started by Xhanch Studio, May 05, 2011, 05:28:41 PM

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Xhanch Studio

May 05, 2011, 05:28:41 PM Last Edit: May 05, 2011, 05:47:33 PM by Xhanch Studio
This type of puzzle can be called as dissection puzzles since you have to divide shapes into a requested shape/goal by following the provided rules.

Here they are:

  • [spoiler=Type 1]

    Divide the figure into four pieces which would be identical in their shape and size.

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 2]

    Divide this irregular chocolate bar into two pieces which, when rearranged, can form an 8x8 square. The divisions must be made along the white lines only.

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 3]

    The checkered shape can be divided into just two parts which can form a perfect solid 8 x 8 checkerboard. How can it be done? Do not overlap the obtained parts.

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 4]

    Into how many pieces should the orange square be divided so that they can be first arranged into the blue "Cocoon" shape and then rearranged into the red "Butterfly" shape? The pieces can be rotated but not overlapped.

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 5]

    Divide the arrow at left into three pieces that could be rearranged into the rectangle at right. The pieces must be different in their shapes and areas. The cuts must go through the lines of the grid. The pieces can be rotated and/or flipped over.

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 6]

    Divide this shape into four identical pieces. The pieces can be mirrored.

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 7]

    An unusual bar of chocolate shown here consists of twenty squares. Can you make four cut so that to divide the bar into nine parts which in turn would form four perfect squares all of exactly the same size? The cuts not necessarily must be done along the provided lines.

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 8]

    Believe it or not, this house-like shape can be successfully divided into just three pieces which can be then rearranged to produce a perfect square. Can you find the solution?

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 9]

    The trapezoid shown in the illustration is called a triamond, or an order-three polyiamond, because it can be formed by joining three equilateral triangles. The challenge is to cut the triamond into four congruent parts. The illustration gives the traditional solution. But it is said there can be different solution found. Though in that solution all four regions do not have the same shape as the larger figure, but they are identical (the parts may be turned over). Can you discover that new solution?

    [spoiler=The answer][/spoiler][/spoiler]

  • [spoiler=Type 10]

    A polygon whose interior angles are equal and whose sides are equal is a regular polygon. Can you cat the regular hexagon shown in the diagram into 12 congruent quadrilaterals?

    [spoiler=The answer][/spoiler][/spoiler]

Best Regards,
Susanto B.Sc
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