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# Red and Blue squares

10 replies to this topic

### #1 bonanova

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Posted 06 August 2012 - 06:41 AM

A table top is tiled with red unit squares, none of them overlapping.
A blue unit square is laid on top.

What is the maximum number of red squares the blue square can touch overlap for some non-zero area?

Edited by bonanova, 06 August 2012 - 07:21 PM.
Clarify touch.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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### #2 Pickett

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Posted 06 August 2012 - 02:03 PM

Spoiler for First (obvious) answer

Edited by Pickett, 06 August 2012 - 02:09 PM.

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### #3 unrealdon

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Posted 06 August 2012 - 02:09 PM

Spoiler for Maximum number of red unit squares that touch the unit blue square

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### #4 Pickett

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Posted 06 August 2012 - 02:12 PM

Spoiler for First (obvious) answer

Spoiler for Alright...My correction

Edited by Pickett, 06 August 2012 - 02:16 PM.

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### #5 bonanova

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Posted 06 August 2012 - 07:19 PM

Good going, but so far no one has the answer.

Clarification about overlap and touching. Apologies to unrealdon.
I used "touch" for red-blue contact, when I meant to say overlap.
I'll edit the OP accordingly.
• Touching at the edges does not count as overlap.
• The red squares cover the table without overlap.
• The blue square must overlap a portion of some number of red squares.
That is, blue and red can't just touch at their edges.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #6 curr3nt

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Posted 06 August 2012 - 08:27 PM

Spoiler for ...

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### #7 plainglazed

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Posted 06 August 2012 - 08:59 PM

Spoiler for how 'bout

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### #8 bonanova

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Posted 06 August 2012 - 09:33 PM

Spoiler for how 'bout

Bingo. Nicely done.

Now we'll just put red squares anywhere on the table, (i.e. let them move apart,) but not overlapping each other.
Can the blue square touch (overlap) even more red squares?

This is counterintuitive, which makes it a good puzzle.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #9 plainglazed

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Posted 07 August 2012 - 12:44 PM

Spoiler for the sake of Spoilers

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### #10 bonanova

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Posted 07 August 2012 - 01:51 PM

That'll do it. Nice.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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