(a) A radio lamp has a 7-contact plug, with the contacts arranged in a circle. The plug is inserted into a socket with 7 holes. Is it possible to number the contacts and the holes so that for any insertion at least one contact would match the hole with the same number?(b) A radio lamp has a 20-contact plug, with the contacts arranged in a circle. The plug is inserted into a socket with 20 holes. Let the contacts in the plug and the socket be already numbered. Is it always possible to insert the plug so that none of the contacts matches its socket? combinatoricscombinatorial geometrygeometry