Consider the following puzzle: how many single, loose, smooth 30 cm bricks are necessary to form a single leaning pile with no part of the bottom brick under the top brick? Begin by considering a pile of 2 bricks. The top brick cannot project further than 15 cm without collapse. Then consider a pile of 3 bricks. Show that the top one cannot project further than 15 cm beyond the second one and that the second one cannot project further than 7.5 cm beyond the bottom brick (so that the maximum total lean is (1/2 + 14) 30 cm). Show that the maximum total lean for a pile of 4 bricks is (1/2 + 1/4 + 1/6)30 cm and deduce that for a pile of n bricks it is

Hence solve the puzzle.

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( 1/2 + 1/1 + 1 2 + ... + 2n + 2) 30 cm.