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21 November
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This puzzle has five unrelated parts.
Show your work.
- In a game of bridge a deck of 52 cards is (randomly) dealt to 4
players around a card table.
Each player gets 13 cards.
Players sitting opposite one another form a team.
So there are 2 teams of 2 players each.
What is more likely, that our team holds all hearts, or that the opposing team
holds all hearts?
- William, a mathematician, and Scott, a theologian among other things,
toss a coin to see who would pay each round of bishop wine.
After a couple of hours William observes that he has won way more times than
Scott, despite the fifty-fifty chances with the coin.
So William offers the following deal.
Scott gets 2 fair coins and William gets 1.
Each time Scott tosses more heads than William, Scott wins.
What is the chance for Scott to win under this novel arrangement?
- On the kitchen table lies a row of 20 coins, a mixture of pennies,
nickels, dimes, and quarters.
Alternatingly Alyssa 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 Alyssa guarantee that she ends up with at least half of the
total value of the coins?
- Recall that a chess board has a size of 8 by 8 squares.
First, try to cover the chess board with dominoes, where each domino has a
size exactly 2 squares in a row.
(Of course you can.)
How many dominoes do you need?
Next, try to cover the original chess board with trominoes, where each tromino
has exactly the size of 3 squares in a row.
If it is impossible, explain why it is impossible.
Finally, try to cover the chess board with trominoes such that exactly one
field is left uncovered.
How many trominoes do you need?
- 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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10 October
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This puzzle has six unrelated parts.
Show your work.
- This one should be very easy.
Find a statement about numbers n that is true exactly when the value of n is
bigger than a hundred.
- "Our math teacher has more than a million good ideas," says Kristin.
"He does not," says Anna, "he has fewer good ideas."
"He has at least one good idea," says Alyssa.
If only one of the 3 statements is true, how many good ideas does our math
teacher have?
- 5 mathematicians from the Netherlands walk along the street.
At once they notice that someone had dropped 10 pennies across the street.
The 5 Dutchmen dash through traffic across the street to pick up these pennies.
All 5 of them end up with a different number of pennies.
How many pennies did each of them end up with, and why?
- This is a puzzle from one of the Simpsons episodes.
Click on this link to see 4 figures.
Add a 5th figure that continues the pattern.
- Click on this link to see 8 figures.
Complete the last row to continue the pattern of the 1st and 2nd row.
- 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?
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