Trick of Mind

Here’s an oldie. I think it’s an excellent logic puzzle.

My wife and I invited four other couples to our New Year’s Eve bash. After yelling “Happy New Year!”, everyone either shook hands with or hugged each other. The couples only hugged each other.

When I asked everyone how many people they shook hands with, each gave a different answer.

How many people did my wife shake hands with?

How many people did I shake hands with?

On TV I heard the western coast line of Antarctica was melting a lot of ice.   Isn’t each part of coast toward the North?

I soon knew which side was “west”, but then I realized, knowing which side is west could be a trick of mind.

If you can figure out this, then which would be the southern coast section?

After some intense card games, Dave decides to order some pizza for the guys to split. Andy needs to use the restroom anyway, so they both get up from the card table. While Bob and Charlie are sitting there waiting for the others to return, Bob comes up with a quick game, and tells Charlie he has a 50%/50% chance of winning.

Bob pulls from the deck a Red Ace, a Black Ace, and a Black Jack. He tells Charlie to blindly pick 2 of the cards. If he chooses both Aces, he wins and Bob has to buy his portion of the pizza! But if he picks the two Black cards he looses and has to pay for Bob’s pizza. However, if he grabs the Red Ace with the Jack, Bob will re-shuffle the cards and let Charlie draw again.

1) Was Bob honest when he told Charlie his chances?
2) On average, how many times would Charlie draw cards until someone is buying the other’s pizza?
3) On average, how many games (including re-shuffles) would Charlie need to play to get a winning hand?
4) On average, how many times would Charlie have to draw cards to get a winning hand?

Andy, Bob, Charlie, and Dave are at it again. Now it is Andy’s turn to deal. For this game he decides to use only the J, Q, and K of each suit (Hearts, Clubs, Spades, and Diamonds). Andy will shuffle the modified deck then deal one card to Bob, then Charlie, then Dave, then himself, Bob again, and so on until all the cards are dealt. There are two hands that win: a flush (all cards the same suit), which beats the other winning hand, a three-of-a-kind. Jacks lose to Queens, which lose to Kings. If no one wins, the cards are shuffled and re-dealt until there is a winner (or a tie). If two or more players have an equal winning hand, it is a tie, (and the game is over).

What is the probability that Dave will win (without a tie) ?

This  “trick of mind” question should not be hard.  Anyone can add their own guess to the list.

We will determine the distance from the first letter to the last.

What word would you guess as the longest word?

When things fall, their speed is limited by friction.  Weight increases the speed, but size generally increases friction.

What about sliding down a mountain?  It seems like that would be much slower than a  fall straight down.  Think about snow.

When it falls, it is very slow.  But I heard that avalanches slide  down a mountain at about 250 miles an hour!  How can that be so fast?

I don’t know the answer.

There are 2011 distinct points on a circle. If you connect two of them to form a line and then connect a different two to form another line, what is the probability that the two lines intersect inside the circle?

Let H and T be the end points of a line 1 unit long. Starting at the centre, flip a coin. If it’s heads then move half way betwen the current position and H. If it’s tails then move half way betwen the current position and T.

On average, how far from the centre will you be after 2009 flips?

How many ways can you make $2010 dollars, using only $2, $5 and $10 notes?

e.g. 5 *$2 + 2*$5 + 1990*$10 or 201*$10.