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The circumference of two concentric disks is divided into 200 sections each. For the outer disk, 100 of the sections are painted red and 100 are painted white. For the inner disk, the sections are painted red or white in an arbitrary manner. Show that it is possible to align the 2 disks so that 100 or more of the sections of inner disk have their colors matched with the corresponding sections on the outer disk.

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