Can a Unit Square be Covered with Six Squares of Side Length Less than 1/2?

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SUMMARY

The discussion centers on the mathematical problem of covering a unit square with six squares, each having a side length of less than 1/2. It is established that while seven squares can successfully cover the unit square, it is impossible to achieve this with only six squares. The problem originates from Newman and is referenced in a posted link for further exploration.

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julien
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Hello,

A problem from Newman, which I posted at
http://www.mymathforum.com/POW/POW1.pdf , asks to show that it is
impossible to cover a unit square with 5 squares whose sides have
lengths <1/2.


It is possible to realize such a covering with 7 squares.


What if we allow us only 6 squares ?


JS,
http://www.mymathforum.com
 
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It's possible with 7 squares, as shown http://www.stetson.edu/~efriedma/squcosqu/" .
 
Last edited by a moderator:
julien said:
A problem from Newman, which I posted at
http://www.mymathforum.com/POW/POW1.pdf , asks to show that it is impossible to cover a unit square with 5 squares whose sides have
lengths <1/2.
how can we prove that? any ideas?
 

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