There are four middle schools in a circular runway clockwise: A 1, A2, A3 and A4. They have 15, 8, 5, 12 color TVs in turn. In order to make the number of color TVs in each school the same, some middle schools are allowed to transfer color TVs to neighboring middle schools, so the number of color TVs that meet the requirements is (65440).

Let A 1 middle school transfer x 1 color TV to A2 middle school (if x 1 is negative, A2 middle school will transfer |x 1| color TV to A 1 middle school, the same below).

A2 Middle School transfers x2 color TV to A3 Middle School; A3 Middle School transfers x3 color TV to A4 Middle School; A4 Middle School Transfers x4 Color TV to A 1 Middle School.

Color TV 15+8+5+ 12=40 sets, with an average of 10 sets per school.

∴ 15-x 1+x4= 10,8-x2+x 1= 10,5-x3+x2= 10, 12-x4+x3= 10∴x4=x 1-5,x 1=x2+2, x2=x3+5,x3=x4-2∴x4=x 1-5,x2=x 1-2,x3=x2-5=x 1-2-5=x 1-7

∵y = | x 1 |+| x2 |+| x3 | | x4 | = | x 1 |+| x 1-2 |+| x 1-7 |+| x 1-。

Where x 1 is an integer satisfying -8≤x 1≤ 15.

Let x 1=x, and consider that the function y = | x |+| x-2 |+| x-7 | | x-5 | is defined as -8 ≤

∫| x |+| x-7 | represents the sum of distances from the number x to 0 and 7. When 0≤x≤7, |x|+|x-7| takes the minimum value of 7;

Similarly, when 2≤x≤5, |x-2|+|x-5| takes the minimum value of 3,

Therefore, when 2≤x≤5, y takes the minimum value 10, that is, when x = 2,3,4,5,

| x1||| x1-2 ||| x1-7 || x1-5 | The minimum value is 10. Therefore, the minimum number of color TV sets to be transferred is 10.