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# If 25 squares, each painted one of the solid colours of red, green, ye

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Joined: 02 Sep 2009
Posts: 52294
If 25 squares, each painted one of the solid colours of red, green, ye  [#permalink]

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30 Nov 2017, 22:03
00:00

Difficulty:

(N/A)

Question Stats:

77% (01:19) correct 23% (00:39) wrong based on 15 sessions

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If 25 squares, each painted one of the solid colours of red, green, yellow, or blue, are lined up side by side in a single row so that no two adjacent squares are the same colour, and
there is at least one square of each colour, what is the maximum possible number of blue squares?

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

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If 25 squares, each painted one of the solid colours of red, green, ye  [#permalink]

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30 Nov 2017, 22:13
Bunuel wrote:
If 25 squares, each painted one of the solid colours of red, green, yellow, or blue, are lined up side by side in a single row so that no two adjacent squares are the same colour, and
there is at least one square of each colour, what is the maximum possible number of blue squares?

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

I chose E, 13.

We can arrange like this : (I put in two lines for convenience)
B is blue and X is green or yellow.

B X B X B X B X B X B X
B X B X B X B X B X B X B

WDYT?
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Re: If 25 squares, each painted one of the solid colours of red, green, ye  [#permalink]

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30 Nov 2017, 22:14
Bunuel wrote:
If 25 squares, each painted one of the solid colours of red, green, yellow, or blue, are lined up side by side in a single row so that no two adjacent squares are the same colour, and
there is at least one square of each colour, what is the maximum possible number of blue squares?

(A) 9
(B) 10
(C) 11
(D) 12
(E) 13

Maximum blue squares can be arranged in an arrangement starting with blue square and ending with blue square alternately (gaps filled with other color squares)

13
E
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If 25 squares, each painted one of the solid colours of red, green, ye  [#permalink]

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30 Nov 2017, 22:15
E

Let the first square be Blue, second be red, third be blue, fourth as yellow, fifth as blue and sixth as green. We have 3 blue square.
Then let the 7th square be blue. And every alternate square (odd numbers) be blue. Hence the number of blue square is 3+(25-7)/2+1 =13.
This is the arrangement that gives the maximum blue squares as per the given criteria.

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If 25 squares, each painted one of the solid colours of red, green, ye &nbs [#permalink] 30 Nov 2017, 22:15
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