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1 May
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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 2013?
- 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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27 February
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This puzzle has four unrelated parts.
Show your work.
- Find the sum 1+2+3+ ... +99+100, and show through your work why the
answer is correct.
(Clever mathematical methods are encouraged.)
- This puzzle consists of 3 parts, each next one slightly more work.
- You are given a balance and 3 identical looking coins.
2 of the 3 coins are pure gold.
The 3rd coin is not pure gold, and is slightly lighter than a proper gold coin.
Show how to use the balance exactly 1 time to determine which of the 3 coins is
the one that is slightly lighter.
No trickeries like putting coins on the scales one at the time, just 1 weighing
allowed.
- You are given a balance and 9 identical looking coins.
8 of the 9 coins are pure gold.
The 9th coin is not pure gold, and is slightly lighter than a proper gold coin.
Show how to use the balance exactly 2 times to determine which of the 9 coins
is the one that is slightly lighter.
No trickeries like putting coins on the scales one at the time, just 2
weightings allowed.
- You are given a balance and 27 identical looking coins.
26 of the 27 coins are pure gold.
The 27th coin is not pure gold, and is slightly lighter than a proper gold
coin.
Show how to use the balance exactly 3 times to determine which of the 27 coins
is the one that is slightly lighter.
No trickeries like putting coins on the scales one at the time, just 3
weightings allowed.
- Click on this link to see 5 figures.
One of these 5 figures is most different from the other 4.
Which one is most different, and why?
- Three cannibals and three missionaries (probably Jesuits) want to cross
the river.
The boat holds at most two people.
The problem is that if on either side at any time the cannibals outnumber the
missionaries, those missionaries will be eaten.
How can all six get to the other side alive?
(Check the web through a search engine for `cannibals and missionaries'.)
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