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What is the maximum number of 3x3 squares that can be formed

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What is the maximum number of 3x3 squares that can be formed [#permalink] New post 30 May 2012, 12:33
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

70% (01:43) correct 30% (00:38) wrong based on 49 sessions
What is the maximum number of 3x3 squares that can be formed from the squares in a 6x6 checker board?
Attachment:
square.jpg
square.jpg [ 30.23 KiB | Viewed 2651 times ]


A. 4
B. 6
C. 12
D. 16
E. 24
[Reveal] Spoiler: OA
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Re: What is the maximum number of 3x3 squares that can be formed [#permalink] New post 30 May 2012, 13:14
say the board is as below (6*6):

1 2 3 4 5 6
2
3
4
5
6

for 3*3: start from 1st row and 3rd row. Using each row we can have maximum 4, 3*3 square.
we can continue the process for (2nd and 4th row) = 4 squares, (3rd and 5th row) = 4 squares, and (4th and 6th row) = 4 squares
Total = 4+4+4+4=16 (3*3)squares
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Re: What is the maximum number of 3x3 squares that can be formed [#permalink] New post 31 May 2012, 03:48
is the answer 16.

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they can be chosen as 4*4 = 16

Top Row: total 4 ways to chose in rows

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1st coloum: Total 4 ways to chose in coloums

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Re: What is the maximum number of 3x3 squares that can be formed [#permalink] New post 31 May 2012, 09:47
Thanks a lot guys. Got it!
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Re: What is the maximum number of 3x3 squares that can be formed [#permalink] New post 28 Jul 2012, 02:43
Is there any direct formula to calculate it?

Thanks in advance !
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Re: What is the maximum number of 3x3 squares that can be formed [#permalink] New post 28 Jul 2012, 03:05
mneeti wrote:
Is there any direct formula to calculate it?

Thanks in advance !


Not really, but no need for a formula.

Think of, for example, choosing your 3 x 3 square by choosing first its left bottom corner. You have to be sure that the upper right corner will still be inside the big board.
It means that you can choose the bottom left corner anywhere in the bottom left area of 4 x 4. Which means 4 x 4 = 16 possibilities.
Or you can concentrate on any other corner of the 3 x 3 square, and then figure out where that corner can be.
I don't think you need to force here some formula saying 4C1 x 4C1 for choosing those corners...or anything similar.

So, answer D.
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Re: What is the maximum number of 3x3 squares that can be formed [#permalink] New post 28 Jul 2012, 06:29
I don't like the structure of this question. The question does not explicitly state how large each square is. I know there is a picture, but the question does not reference the picture at all.
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Re: What is the maximum number of 3x3 squares that can be formed [#permalink] New post 26 Aug 2012, 16:16
+1 D

Imagine that tou have a 3x3 square and how you could placed it on that board.
You have to respect the edges or borders ;)
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Re: What is the maximum number of 3x3 squares that can be formed [#permalink] New post 12 Sep 2014, 00:25
Answer = 4 * 4 = 16

Refer diagram below:
Attachment:
square.jpg
square.jpg [ 52.28 KiB | Viewed 238 times ]

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Re: What is the maximum number of 3x3 squares that can be formed   [#permalink] 12 Sep 2014, 00:25
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