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23 March
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This puzzle has four unrelated parts.
Show your work.
- We want to time the boiling of an egg for 6 minutes.
All we have is a 4-minute hourglass and a 5-minute hourglass.
What is the quickest way to measure the 6 minutes?
- Let us count on the fingers of our left hand as follows.
Our little finger is 1, our ring finger is 2, our middle finger is 3, our
index finger is 4, and our thumb is 5.
Keep counting by moving in the opposite direction:
The index finger is 6, the middle finger is 7, the ring finger is 8, and the
little finger is 9.
Keep counting by again reversing direction;
The ring finger is 10, the middle finger is 11, and so on, each time reversing
direction.
Which finger do we end on when we count to 2015?
- Click on this link to see this puzzle.
- We are given 12 identical matches.
We can arrange them as edges of polygons in many ways, like:
- When we line them up as boundaries of a square with sides 3, then the
enclosed area equals 9.
- When we line them up as boundaries of a rectangle of width 5 and
height 1, then the enclosed area equals 5.
- If we arrange them as boundary of the blue area below, then the
enclosed area equals 5.
Find a polygon arrangement such that the enclosed area equals 6.
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9 February
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This problem set has unrelated parts.
Show your work.
- Give the Banzhaf power distribution of the weighted voting system
[5; 4, 1, 1, 1].
- Give the Shapley-Shubik power distribution of the weighted voting system
[5; 4, 1, 1, 1].
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