MIT6_042JF10_rec12

# MIT6_042JF10_rec12 - 6.042/18.062J Mathematics for Computer...

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6.042/18.062J Mathematics for Computer Science October 20, 2010 Tom Leighton and Marten van Dijk Problems for Recitation 12 1 The L-tower problem Observe the structures shown in Figure 1 . One has 2 L-shapes, the other 5 L-shapes. Con- sider a tower with k L-shapes. Assume that the blocks are all of size x × 1 where x > 1. As the picture indicates, if k is too small then the tower falls to the left. On the other hand, if k is too large the tower would fall to the right. Will the tower be stable for some k ? Prove there is at least one value of k for which the L-tower is stable. Assume that a structure is stable if and only if its center of gravity is not hanging in the air horizontally. The L-tower is stable if and only if each of its subparts is stable. Hint: Show the tower is stable if and only if 3 x 2 3 k 3 x 2 1 . Figure 1: Too few or too many L shapes make the tower unstable

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± ± ± Recitation 12 2 2 Double Sums Sometimes we have to evaluate sums of sums, otherwise known
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MIT6_042JF10_rec12 - 6.042/18.062J Mathematics for Computer...

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