Cutting a Square Board

[tonebeeze]

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

[anshumishra]

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.



[/spoiler]

[srcc25anu]

8

3 sq of size 2*2
1 sq of size 3*3
4 sq of size 1*1

[tonebeeze]

OA = [spoiler](D) 8[/spoiler]

[Anurag@Gurome]

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.