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# In 25 squares, each painted one of the solid colors red,

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Eternal Intern
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In 25 squares, each painted one of the solid colors red, [#permalink]  17 Jul 2003, 12:32
In 25 squares, each painted one of the solid colors red, green, yellow, or blue, are lined up side by side in a single row so that no two adjacent squares are the same color and there is at least one square of each color, what is the maximum possible number of blue squares?

Last edited by Curly05 on 18 Jul 2003, 17:38, edited 1 time in total.
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Need Explanation! [#permalink]  17 Jul 2003, 14:09
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Brainless wrote:
12

how about 13. Since the square are in a row, there is no reason why the blue ones can't be in all of the odd positions.
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
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AkamaiBrah wrote:
Brainless wrote:
12

how about 13. Since the square are in a row, there is no reason why the blue ones can't be in all of the odd positions.

Nah.. My reasoning is simple.

Since we must have one of each kind including ONE BLUE, we are left with 21 squares. And since we need to alternate colors, we can have another 11 BLUE maximum. Altogether we have 12 BLUES. This is true for any color ..

Am I missing some thing ?

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Brainless

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Brainless [#permalink]  17 Jul 2003, 17:11
Can an algebra formula be done listing out the possible squares? Remember, Brainless, we have about two minutes to get solution.

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13 is correct.
Eternal Intern
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How long it take you [#permalink]  17 Jul 2003, 18:55
How long it take you?
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also vote for 13

B_B_B_B_ .... _B

among all Bs there are enough free places to put G, Y, and R.

So, the maximum number of blue squares is the number of odds in 25.
13 odd+12 even

Thus, 13.
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Re: Is this an Algebra or Geometry Challenge [#permalink]  18 Jul 2003, 17:02
Curly05 wrote:
In 25 squares, each painted one of the solid colors red, green, yellow, or blue, are lined up side by side in a single row so that no two adjacent squares are the same color and there is at least one square of each color, what is the maximum possible number of blue squares?

Note the words in bold, in your question. Now once that is known, all one has to know is that there should be one more color apart from Blue to make sure that the color Blue does not come in adjacent boxes.

Finish!!!!!!!!!!!!!

You have the solution 13
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Rationale [#permalink]  18 Jul 2003, 17:52
If you count all the numbers
1.3.5.7,9, 11,13, 15, 17, 19, 21, 23, 25- there are 13.

But 3 out of every five squares is blue and there are 25 squares.

3 x
-- = ----
5 25

Why is this wrong?

There are x-squares
x -1 - stand for?
2x-1=26
x=13
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Attention [#permalink]  21 Jul 2003, 06:11
Why isn't my ratio working?
Eternal Intern
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Cmon, Akami, show me why ratio isn't working?
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Victor,
The ratio is not working because:
In the first 5 sq., you have 3 blue sq
In the next 5 sq., you have 2 blue sq.
In the next 5 sq., you have 3 blue sq
In the next 5 sq., you have 2 blue sq.
In the next 5 sq., you have 3 blue sq

So, altogether u have 3+2+3+2+3= 13

Because the # of blue sq. is varying, your ratio is not working
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prakuda2000 wrote:
Victor,
The ratio is not working because:
In the first 5 sq., you have 3 blue sq
In the next 5 sq., you have 2 blue sq.
In the next 5 sq., you have 3 blue sq
In the next 5 sq., you have 2 blue sq.
In the next 5 sq., you have 3 blue sq

So, altogether u have 3+2+3+2+3= 13

Because the # of blue sq. is varying, your ratio is not working

Victor,

You would have seen that yourself if you had made a little effort and drawn a picture....
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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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