KöMaL 2011 B4373

An international conference of polypodal creatures is organized on the top of the Glass Mountain. The numbers of legs of the participants, $a_1$,...,$a_n$, all are positive even numbers. The side of the Glass Mountain is slippery. Each of the creatures gathering at the base of the mountain can only get to the top if they wear special climbing shoes on at least half their feet. At least how many shoes are needed altogether to get all participants up to the top if a shoe must always be worn on a foot when it travels up or down the mountain?