There is a kind of round cake, which can only be cut vertically downward, but not horizontally. How many pieces can I have at most for 20 dollars?
Don't draw: 1 straight line divides the plane into two parts at most; Two straight lines divide the plane into four parts at most; Three straight lines divide the plane into seven parts at most; Now add a fourth line. It has at most three intersections with the first three straight lines. These three intersections divide the fourth straight line into four segments, and each segment divides the original plane into two parts, so the four straight lines divide the plane into 7+4= 1 1 at most. Similarly, five straight lines divide the plane into 1 1 at most. Six straight lines divide the plane into at most 16+6=22 parts; Generally, n straight lines divide a plane into 2+2+3 at most. +n = (n squared +N+2)/2, so the answer is (36+6+2)/2=22.