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Some Juicy Geometry Puzzles - Assignment | MATH 102, Assignments of Mathematics

State University of New York (SUNY) - PotsdamMathematics
Prof. Jason Howald

Material Type: Assignment; Professor: Howald; Class: MATH FOR ELEMENTARY ED II; Subject: MATHEMATICS; University: SUNY-Potsdam; Term: Unknown 2007;

Typology: Assignments

Pre 2010

Uploaded on 08/09/2009

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Math 102, Some Juicy Geometry Puzzles!
Classroom work:
(1) It’s easy to divide a square into four smaller squares, or even nine squares::
If we allow the squares to be not all the same size, can you divide a square into six squares? What about five?
Seven? How many other numbers can you get?
(2) Given a 3 ×3 grid of dots, is it possible to draw four straight line segments which together go through all the dots,
without lifting your pencil?
· · · · · · · · · · · ·
· · · · · · · · · · · ·
· · · · · · · · · · · ·
(3) In order to supply utilities (water, electricity, and gas) to three new campsites in the Happy Camper RV Development,
you must connect to each campsite with pipe or wire. For safety reasons, you want the connections (pipe and wire)
not to cross. Can you arrange three utility stations and three campsites without crossing the connections?
pf2

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Download Some Juicy Geometry Puzzles - Assignment | MATH 102 and more Assignments Mathematics in PDF only on Docsity!

Math 102, Some Juicy Geometry Puzzles!

Classroom work:

(1) It’s easy to divide a square into four smaller squares, or even nine squares::

If we allow the squares to be not all the same size, can you divide a square into six squares? What about five? Seven? How many other numbers can you get?

(2) Given a 3 × 3 grid of dots, is it possible to draw four straight line segments which together go through all the dots, without lifting your pencil?

(3) In order to supply utilities (water, electricity, and gas) to three new campsites in the Happy Camper RV Development, you must connect to each campsite with pipe or wire. For safety reasons, you want the connections (pipe and wire) not to cross. Can you arrange three utility stations and three campsites without crossing the connections?

(4) What is larger – the area of the inner, darkest-shaded circle (labeled A), or the area of the outermost white annulus (labeled B)?

(5) Four towns (A-ville, B-burg, C-ton and D-borough) happen to be arranged in a perfect square, but sadly there are no roads between them. If pavement is very expensive, you might want to connect all four towns using a minimum amount of road, even if it means forcing people to drive farther than they might want to. How can all four towns be connected with the least amount of road?

(6) Right triangles with integer coordinates can be obtained by finding three integers a, b, c with a^2 + b^2 = c^2. The simplest choice is the 3, 4 , 5, but there are others, like 5, 12 , 13 , and 20, 21 , 29. Can you find more? Are there any patterns among the ones you can find?