Constructing Rectangles With Jigsaw Puzzle

What is the smallest rectangle which can be made by using jigsaw pieces of these two shapes only?

jigsaw

What is the next smallest such rectangle?

What rectangles are possible using these shapes only?

(Note: You can use no matter how many of these two jigsaw pieces as you see fit.)

Solution

There is more to this jigsaw than first meets the eye. The smallest possible rectangle is 6 × 3 as shown here,

jigsaw2

and by using this as a basic building block an infinite sequence of larger rectangles can easily be generated. The next smallest rectangle is a 12 × 3 or a 6 × 6 formed by using two of the above rectangles, but the third order of size is not a 9 × 6 or 18 × 3 but a 10 × 5 as shown.

jigsaw3

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About Edmark M. Law

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. I blog at learnfunfacts.com. You can find me on Twitter @EdmarkLaw and Facebook. My email is edmarklaw@learnfunfacts.com
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5 Responses to Constructing Rectangles With Jigsaw Puzzle

  1. Thank you for exercising my mind!

    Like

  2. Jack Shalom says:

    When I was a child, a favorite aunt bought me a copy of Solomon Golumb’s book, Pentominoes, which came complete with a set of plastic pentominoes. Those shapes have intrigued me ever since.

    Like

  3. Alfie says:

    that was good

    Like

  4. Miriam says:

    I wish I had more of a mathematical mind. You stumped me!

    Like

  5. Viola Bleu says:

    Nope. I tried and you lost me. That’s no reflection you, because I love a puzzle. It’s more about my brain and eyes forgot to rejoin their fibres following a vodka martini last night. How did Bond even do those???

    Like

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