拆解彩虹贝果
Disassembled Rainbow Bagel
题目详情
Seven concentric circles, each of integer diameter, are used to determine six annuli, as shown below. The annuli have a total area of 2019π.
The annuli are then cut into quarters, and these 24 quarter-annuli are rearranged to form the two loops shown below.
What is the difference between the enclosed areas of the two loops?
解析
Original Explanation
The answer to this month’s puzzle is π−1.
The loops can be dissected into overlapping rectangles, quarter-circles, and a central square as shown. Furthermore, it can be shown that the diameters of the seven circles are 670, 671, 672, 673, 674, 675, 676. From here it is a matter of properly adding (and occasionally subtracting) the various component areas to get the correct answer.