Round 2

1. The following diagram depicts three views of the same solid. The solid was made from a cylinder of wood, with a height of 1 and a diameter of 1. Then four "corners" were rasped off, and it was painted. As a result, from above, the solid has a circular silhouette of diameter 1; from the front, it has a square silhouette of side length 1; from the side, it has a square silhouette (rotated 45 degrees) of side length SQRT(0.5).

What is the volume of the solid?

2. Find four letters that can be arranged into six different four-letter words that aren’t proper nouns or abbreviations, and can be found at www.dictionary.com. (Different meanings of the same spelling do not count.)

3. Consider this series:

4, 5, 8, 8, 9, 9, 12, 13, 13, 13, 17, 18, …, …, …

What would the 50th, 63rd and 100th observations be?

4. You have a hand of cards that depict each of the letters of the alphabet. You fan the cards and see they are in the following order:

F, W, X, Y, Z, K, L, A, T, U, J, N, O, S, D, E, P, V, C, B, G, H, I, Q, R, M

Your job is to put the cards in alphabetical order in the minimum number of moves. You may remove any number of consecutive cards and insert them anywhere else in the fan; this counts as one move. Of course, you must preserve the order of the cards you move, and keep all cards facing the same way.

Describe how you rearrange the cards in this (example) format:
1. Move D-K to between S and T.

5. Carl has a psychological disorder whereby he takes everything literally. He is also incredibly obedient; if you tell him to "hop to it", he will actually hop.

When he was out walking in the park recently, he came upon a sign. When he read the sign, he looked about, spotted a gardener, and approached him.

"Excuse me," he said to the gardener with an air of defiance. "There is no way you're going to get me into one of those bins."

The bewildered gardener followed Carl's pointing finger to an ordinary garbage bin.

What did they sign say to cause Carl to behave so strangely?

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