Let’s talk about spinning plates! A juggler wants to perform a trick where he will spin three platesas long as possible. Suppose that a plate of type k starts the plate spinning trick by spinning at k rotations per second. Every plate slows down by one rotation persecond each second. Whenever needed, the juggler can increase thespin rate of a plate of type k,by krotationsper second. If the plate’s speed is not increased before or at theinstant its spin rate reaches zero, it falls off its support andends the trick. The juggler can perform at most one “boost†ofspeed to one plate at the end of each second during the trick.Determine the unordered triples (a,b,c)of positive integers such that the juggler can keep three plates,of types a,b,and c,spinning indefinitely.
