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Cutting a Square Board

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by tonebeeze » Fri Mar 11, 2011 11:27 am
A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut?

a. 5
b. 6
c. 7
d. 8
e. 9
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by anshumishra » Fri Mar 11, 2011 11:39 am
tonebeeze wrote:A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut?

a. 5
b. 6
c. 7
d. 8
e. 9
Made mistake, here is how it will work. 8 squares.


Image
[/spoiler]
Last edited by anshumishra on Fri Mar 11, 2011 11:54 am, edited 1 time in total.
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by srcc25anu » Fri Mar 11, 2011 11:40 am
8

3 sq of size 2*2
1 sq of size 3*3
4 sq of size 1*1
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by tonebeeze » Fri Mar 11, 2011 11:49 am
OA = [spoiler](D) 8[/spoiler]
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by Anurag@Gurome » Fri Mar 11, 2011 8:28 pm
tonebeeze wrote:A square board that has an area of 25 square inches is to be cut into pieces, each of which is a square with sides of length 1, 2, or 3 inches. What is the least number of such square pieces into which the board can be cut?

a. 5
b. 6
c. 7
d. 8
e. 9
Solution:
The area of the square board is 25 square inches.
So, the side is sqrt 25 = 5 inches.
Now with a side of 5 inches, we cannot have more than 1 square board with side 3 inches.
To explain further, two square boards will make side 3+3 = 6 > 5, which is not possible.
So, we have 1 square board with side 3 inches.
Hence, the area of remaining board is 25 - 9 = 16 inches.
Let the number of square boards with sides 1 inch be x and the number of square boards with side 2 inches be y.
Or, x+4y = 16.
Remember, x and y are positive integers whose sum is minimum.
Minimum possible combination is x = 4 and y = 3.
This makes the total number of square boards as 4+3+1 = 8.
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