Paula:
"Nowhere" can be "Now-here" if you want to look at it that way, and I did.
Now, that's what I call lateral thinking.
For the less enlightened, there is;
The point in the Atlantic Ocean where the Prime Meridian crosses the Equator off the Bight of Africa.
Liessa:
Month:
I'm not sure, but it should the month when daylight savings begins. Over here, that's in March, so I'm guessing May (seems late for that)
Now I can not ask the same question about the Netherlands.
The months of January, March, May, July, August, October and December all have 31 days, but October has an extra hour in it because of the switch back from Daylight Saving Time, making it the longest month of the year. (USA)
Liessa, you know far too much, you should party more.
1. 116 years (there's a series of Dutch books I've read about 200 times about this war )
2. Equador
3. sheep
4. November. There was a big thing about switching calenders. The revolution was in October in one calender, and in November in the other one.
5. Squirrel
6. Dogs. Canus is Latin for dog, there were many dogs when the islands were discovered.
7. Albert. Queen Victoria has asked that no kings were named Albert anymore.
8. red
9. New Zealand
Mark:
IRRATIONAL
sqrt(2) * sqrt(8) = sqrt(16) = 4
Clean and simple.
What is your opinion on:
Let Z=\sqrt{2}\sqrt{2} and Y=\sqrt{2}.
If Z is irrational, then X=Z, and XY = [\sqrt{2}\sqrt{2}]\sqrt{2}=2 is rational, or If Z is rational, then X=Y, and XY is Z, so is rational.
COUPLES
yes and no (but neither did I)
My spouse and I each shook the same three hands - one each from the other three couples.
Every time I think one question has passed you by, you continue to amaze. I think you have the jest of it.
We begin with what we know: since nobody shook hands with more than six persons, and the seven people other than yourself all shook hands with a different number of people, the numbers must have been:
0,1,2,3,4,5,6, respectively.
Let us begin with "0"--whom we shall call the introvert, because this person shook nobody's hand. At the other extreme was "6"--whom we shall call the extrovert for obvious reasons. The extrovert shook everybody's hand, except his/her own spouse. Since the extrovert and the introvert did not shake hands, the introvert must be the extrovert's spouse.
0&6 are a couple, leaving 1,2,3,4,5 and yourself.
Consider the remaining five people other than yourself. Each of these shook hands with the extrovert, and none with the introvert.
One of these five people-- "1", the quasi-introvert--only shook hands with one other person, the extrovert. Another--"5", the quasi-extrovert--shook hands with five people, everyone except his/her own spouse and the introvert ("0").
Therefore, the quasi-introvert and the quasi-extrovert form a couple. 0&6, 1&5 are couples, leaving 2,3,4 and yourself.
In the same way, "2" and "4" form a couple--we'll call them the pseudo-introvert and pseudo-extrovert, respectively.
0&6, 1&5, 2&4 are couples, leaving 3 and yourself.
Therefore, your spouse is the one who shook hands with three other persons. Furthermore, you and your spouse shook hands with the same people: the extrovert ("6"), the quasi-extrovert ("5"), and the psuedo-extrovert ("4"). This gregarious group includes Pat (one of our givens: you shook hands with Pat), and therefore must exclude Chris.
Answer: Your spouse shook hands with Pat, but not Chris.
You must help Pete the pancake chef! He's desperately trying to sort his pancakes by size. How many flips will it take?
There is a stack of N pancakes -- each one a different size -- on top of the griddle. Your goal is to get the pancakes in a stack arranged by size, with the largest pancake on the bottom, smallest one on top. You must accomplish this by flipping the pancakes a limited number of times.
For each flip, you must (on Pete's behalf):
Choose a number k between 1 and N. Pick a pancake in the kth position (counting from the topmost pancake) and insert your spatula under it (between the pancakes in position k and (k+1). Then flip the pancakes on your spatula, reversing the order.
Example:
N=5 (Numbers on the pancakes represent the size of the pancake, not its position.) The smallest pancake is labelled "1":
Initial position: Top 1 3 5 2 4 Griddle
First move (k=3)
Yields: Top 5 3 1 2 4 Griddle
Second move (k=5) Yields: Top 4 2 1 3 5 Griddle
Third move (k=4) Yields: Top 3 1 2 4 5 Griddle
Fourth move (k=3) Yields: Top 2 1 3 4 5 Griddle
Fifth move (k=2) Yields: Top 1 2 3 4 5 Griddle
We used 5 moves to sort the stack.
Here's what I want you to tell me:
For a given N, what is the least number of flips with which you can guarantee that you will correctly sort the stack
For every N, for every initial position, can it be done in N flips
How many flips could be required for a given N and the worst possible initial position
In other words, if we consider N to be fixed, for each initial permutation, there is some minimum number of flips that works. Find the maximum of these minima as you vary the permutations, i.e. find a hardest permutation.
E.g. if N=5, the permutation (Top 2,1,3,4,5 Griddle) would require only one flip, although you could take a roundabout path and take 13 flips. The minimum for this permutation is 1. The minimum for the permutation (Top 1 3 5 2 4 Griddle) is 5 flips as shown. It turns out that any other permutation can also be done in 5 flips. So 5 is the answer.
Or, to put this in simple mathematical terms: For N=number of pancakes, p=permutation Let f(N,p) be the minimum number of flips when faced with initial permutation p; let g(N) be the maximum of f(N,p) over choices of p. Find g (N).
Although this problem may appear simple at first, the solution is actually fairly complex.
Surveys, don't you just hate them?
Q: According to surveys, men are THREE TIMES more likely to be afraid of one of these. What are they more likely than women to be afraid of
Q: According to one survey, one of the fastest growing job markets in the U.S. is not in technology or health care. What is it in
Q: 37% of us decide on the spot, 25% of us think about this days in advance, and 37% decide the day of. What are we so impulsive about
)
