(1) Make a rectangle with three rows and five columns, or three columns and five rows, and arrange two works next to each other.
(2) Make a square with 4 rows and 4 columns, and arrange 1 works nearby.
(3) First make a rectangle with three rows and six columns, or six columns and three rows, in which 1 works need to be arranged less.
The circumference of the three arrangements is 36 decimeters, and the minimum number of colored bars is used.
In practical application, the corresponding layout can be selected according to the calculation results and aesthetic principles.
Analysis:
17 is a prime number. You can use the adjacent composite number 15, 16 or 18 to find the factor, and then add and subtract to get 17, and get the arrangement of works. According to the perimeter formula of the rectangle, the corresponding perimeter is obtained, and the perimeter = (length+width) * 2.
( 1)3*5+2= 17; First make a rectangle with three rows and five columns, or three columns and five lines, and arrange two works nearby. The convex figure needs to add the length of the protruding edge.
The length of a rectangle is 5 * 2 = 10, the width is 3 * 2 = 6, and the circumference is 32. The total circumference of two adjacent sides is 36.
(2)4*4+ 1= 17; First, make a square according to 4 rows and 4 columns, and arrange 1 works nearby.
The circumference of a square is 8 * 4 = 32, plus two adjacent sides of 1, the total circumference is 36;
(3)2*8+ 1= 17; First, arrange a rectangle in two rows and eight columns, or eight columns and two rows, and arrange 1 works nearby.
The length of the rectangle is 8 * 2 = 16, the width is 2 * 2 = 4, the perimeter is 40, and the total perimeter of the two sides adjacent to 1 is 44;
(4)2*9- 1= 17; First, arrange it into a rectangle with two rows and nine columns, or nine columns and two rows, among which 1 works need to be arranged less. The works smaller than 65,438+0 form a concave figure with the same circumference as the rectangle.
The rectangle is 9 * 2 = 18 in length, 2 * 2 = 4 in width and 44 in circumference.
(5)3*6- 1= 17; First put it into a rectangle with three rows and six columns, or six columns and three rows, among which 1 works need to be arranged less. The works smaller than 65,438+0 form a concave figure with the same circumference as the rectangle.
The rectangle is 6 * 2 = 12 in length, 3 * 2 = 6 in width and 36 in circumference.
To sum up, according to the three methods (1), (2) and (5), the circumference is 36 decimeters, and the number of colored stripes used is the least. According to the calculation, the corresponding layout can be selected according to the aesthetic principle.
Extended data:
The arrangement of 17 works, because 17 is a prime number. You can use the adjacent composite numbers 15, 16 or 18 to find the factor, and then add or subtract 1 or 2 to get 17. Using the obtained factor as the length and width of the rectangle, the perimeter is calculated according to the rectangle perimeter formula. Among them, the convex shape needs to add the protruding side length; The circumference of the concave figure is the same as that of the rectangle. You can get the following five situations:
( 1)3*5+2= 17;
First make a rectangle with three rows and five columns, or three columns and five lines, and arrange two works nearby. Total circumference 36;
(2)4*4+ 1= 17;
First, make a square according to 4 rows and 4 columns, and arrange 1 works nearby. Total circumference 36;
(3)2*8+ 1= 17;
First, arrange a rectangle in two rows and eight columns, or eight columns and two rows, and arrange 1 works nearby. Total circumference 44;
(4)2*9- 1= 17;
First, arrange it into a rectangle with two rows and nine columns, or nine columns and two rows, among which 1 works need to be arranged less. The circumference is 44;
(5)3*6- 1= 17;
First put it into a rectangle with three rows and six columns, or six columns and three rows, among which 1 works need to be arranged less. The circumference is 36;
Comparing the perimeters of the five cases, the perimeters of (1), (2) and (5) are 36 decimeters, which requires the least number of colored stripes.
It can be found that when the length and width of a rectangle are close, its circumference is smaller.
In practical application, the corresponding layout can be selected according to the calculation results and aesthetic principles to make it relatively beautiful.