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17 November
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This puzzle has four unrelated parts.
Show your work.
- A student on her way to Rome reaches a fork in the road.
One way continues to Rome, and the other is a dead end.
Luckily there sit on a bench two people, named William and David.
Unfortunately one of them always lies.
Fortunately one of them always tells the truth.
She knows not which one is the truth teller, and which one is not.
What one question should she ask to one of the people to get the correct answer
for her quest for the way to Rome?
- Click on this link to see the second
puzzle.
- On the kitchen table lies a row of 30 coins, a mixture of pennies,
nickels, dimes, and quarters.
Alternatingly David and William take one coin from the table, but with the
condition that each can only take a coin from either end of the row.
How can beginner David guarantee that he ends up with at least half of the
total value of the coins?
- William, a logician, and David, a computation scientist among other
things, toss a coin to see who would pay each round of alcohol-free beer.
After a couple of hours William observes that he has won way more times than
David, despite the fifty-fifty chances with the coin.
So William offers the following deal.
David gets 2 fair coins and William gets 1.
Each time David tosses more heads than William, David wins.
What is the chance for David to win under this novel arrangement?
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10 October
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This puzzle has four unrelated parts.
Show your work.
- Find the sum 1+2+3+ ... +199+200, and show through your work why the
answer is correct.
(Clever mathematical methods are encouraged.)
- 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 2014?
- Click on this link to see 8 figures.
Complete the last row to continue the pattern of the 1st and 2nd row.
- In the dark of the night four people have to cross a rickety suspension
bridge over a deep ravine.
The bridge carries at most 2 people at a time, and the group has only one
lantern.
It takes Kristen 1 minute to cross the bridge.
It takes Anna 2 minutes to cross the bridge.
It takes Alyssa 5 minutes to cross the bridge.
It takes William 10 minutes to cross the bridge.
How can all cross the bridge in the least amount of time?
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