Martin Gardner's "The Annotated Alice," and Robin Wilson's "Lewis Carroll in Numberland" led the authors to put this article in a fantasy setting. Alice, the March Hare, the Hatter, and the Dormouse describe a straightforward, elementary algorithm for counting the number of ways to fit "n" identical objects into "k" cups arranged in a circle. The authors call these cyclic arrangements Mad Tea Party ("MTP") partitions. Our algorithm enumerates "MTP" partitions (in sets of odd and even entries), then, by ordering them and striking out duplicates, one obtains the ordinary partitions for any positive integer "n."