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12 November
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This puzzle has three unrelated parts.
Show your work.
- A ten-story student residence has identical stairs between its floors.
How many times does it take to climb from the first to the tenth floor as it
is to climb from the first to the fifth floor?
- In 1980 an oldtimer tells his grandchildren that he was n years old in
the year n^2 (n squared).
When was the oldtimer born?
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(a)
Behind a screen I put three cards on a table, a King of hearts, a Queen of
hearts, and a Jack of hearts.
If all faces are up or if all faces are down, I'll yell JACKPOT.
You are allowed to give me instructions to flip one particular card, for
example instruct me to flip the Queen.
Find a shortest list of such instructions to guarantee that I'll yell JACKPOT
at least once.
(b)
The same question as in (a) above, except that I'll only yell JACKPOT when
all cards are face up.
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27 September
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This puzzle has three unrelated parts.
Show your work.
- Eight thousand eight hundred and eight dollars can be properly written
as $ 8808.
How can nineteen thousand nineteen hundred and nineteen dollars be written
down in such a proper way?
- 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 2010?
- Alice and Bill decide on who buys the next round of non-alcoholic beers
by flipping a fair coin.
So both have equal chance to win and have the other buy.
Alice is happy to win a couple of times in a row.
Now she proposes to change the betting rules.
She takes 1 fair dime and Bill takes 2 fair dimes.
The proposed new rules are:
If Bill scores more heads with his 2 dimes, then he wins and Alice buys the
next round; otherwise Bill loses and buys himself.
What are their chances of winning?
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