Mr. Hilbert is busy renovating his hotel. The hotel rooms are going to be made larger, which means that there will be excess beds, furniture etc. that will be sold. For every ten items of one kind one will be sold. His workers went about emptying the rooms one by one, for every ten items of one kind, one was shipped away. When he visited his hotel to see how things are progressing, he was shocked to see that all items had been sold.
His workers, however, assured him that they stuck to his system of selling only one out of ten items taken from the hotel. All items taken from the hotel were moved to a storage site, when ten new items of one kind were moved there, one item of the same kind from the storage site was sold. The question then is how all items can end up having been sold if only one item out of ten taken from the hotel is going to be sold.