2018-02-12 Basic

         

Which triangle has the greatest area?

A well-built square table distributes its weight equally on its four legs. Now, one of the legs is removed. By symmetry, the weight on leg A would be the same as on leg C. How much of the table's weight is supported by leg B?

\[ \large \sqrt{ 2^{ \sqrt{2} } } = \, ? \]

Alice, Bob, and Carol—who always tell the truth and are perfectly logical—have a box with two black hats and two white hats.

Each person is randomly assigned a hat such that they can see the other two people's hats but not their own.

Alice says, "I do not know the color of my hat."

Can Bob and Carol now figure out their own hat colors?

Note: The three logicians are close friends, so each of them knows that they are all perfectly logical and always tell the truth. "Now know" means they know at that moment, without any further events or communication occurring.

The figure at right consists of 3 identical circles which pass through each others' centers.

If the thicker, outer perimeter has length 12, what is the circumference of one of the 3 identical circles?

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