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You want to place n items on the bookshelf in such way that on the top...

You want to place n items on the bookshelf in such way that on the top shelf you have only one item and the number of items double on each consecutive shelf, see below. Justify using the definition of the floor function that it enough to have ⌊log2 n⌋ + 1 of the shelves to place all n items. Consider n = 1,2,3,4,...

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Hint: Assume that the number of shelves is l. Provide the formula for the maximum number of items and minimum number of items that can be placed on the lth shelf when the remaining l − 1 shelves are already filled.

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