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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.

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. _________________

Best,

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

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 ..

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.

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, 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.... _________________

Best,

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