April 2010
62 posts
Salaries
Three coworkers would like to know their average salary. how can they do it, without disclosing their own salaries?
Solution
How about: Person A writes a number that is her salary plus a random amount (AS + AR) and hands it to B, without showing C. B then adds his salary plus a random amount (BS + BR) and passes to C (at each step, they write on a new paper and don’t show the 3rd person)....
World Series
You have $10,000 dollars to place a double-or-nothing bet on the Yankees in the World Series (max 7 games, series is over once a team wins 4 games).
Unfortunately, you can only bet on each individual game, not the series as a whole. how much should you bet on each game, so that, if the yanks win the whole series, you expect to get 20k, and if they lose, you expect 0?
Basically, you know that...
100 Factorial
how many trailing zeroes are there in 100! (100 factorial)?
Solution
One per factor of 10, and one per factor of 5 (there are more than enough 2’s to pair with the 5’s), plus one per factor of ten squared (one occurrence) and one per factor of 5 squared (three occurrences).
So if I’m counting correctly, that’d be 10 + 10 + 1 + 3== 24 zeroes.
Assuming the question meant...
Oil Mogul
You are an oil mogul considering the purchase of drilling rights to an as yet unexplored tract of land.
The well’s expected value to its current owners is uniformly distributed over [$1..$100]. (i.e., a 1% chance it’s worth each value b/w $1..$100, inclusive).
Because you have greater economies of scale than the current owners, the well will actually be worth 50% more to you than to...
Vienna
It’s the middle ages, you’re travelling across europe and you want to find the way to vienna. you come to a crossroads, now there are two ways to go. at the crossroads stand a knight and a knave. the knight answers every question truthfully. the knave answers every question falsely. you don’t know which guy is which. how can you figure out which road leads to Vienna by only...
Duel
You find yourself in a duel with two other gunmen. you shoot with 33% accuracy, and the other two shoot with 100% and 50% accuracy, respectively. the rules of the duel are one shot per-person per-round. the shooting order is from worst shooter to best shooter, so you go first, the 50% guy goes second, and the 100% guy goes third.
where or who should you shoot at in round 1?
Solution
You have 3...
Hen
If a hen and a half lay an egg and a half in a day and a half, how many hens does it take to lay six eggs in six days?
Solution
If 1.5 hens lay 1.5 eggs in 1.5 days (or 36 hours) then: 1 hen lays 1 egg in 1,5 days or 4 eggs in six days thus 1.5 hens lay 6 eggs in 6 days
Box 'o Numbers
Arrange the numbers 1 to 8 in the grid below such that adjacent numbers are not in adjacent boxes (horizontally, vertically, or diagonally):
___ | 1 | ============= | 6 | 4 | 3 | ============= | 2 | 7 | 5 | ============= | 8 | =====
The arrangement above, for example, is wrong because 3 & 4, 4 & 5, 6 & 7, and 7 & 8 are adjacent.
Solution
The...
Coin Problem
some of you may have easily solved the pill weighing problem posed here. If so, you are going to love this problem. It is similar but much more difficult.
from my buddy Tom:
Ok, here’s a tough one (i thought). There are no “aha!” tricks - it requires straightforward deductive-reasoning.
You have 12 coins. one of them is counterfeit. All the good coins weigh the same, while the...
Parallel Lines
Solution
Not really much to solve :)
Moving Circles
Solution
You may be able to find the solution on the discussion forum.
Black Dots
Solution
You may be able to find the solution on the discussion forum.
X Implies Y
Part I
(you can’t use paper, you have to figure it out in your head)
i have a black triangle, a white triangle, a black circle and a white circle. if i gave you a shape (triangle or circle) and a color (black or white), the “frobby” items would be those that had either the shape or the color, but not both. that is, in order to be frobby, the item must be of the specified...
XOR using NAND gates
Create an XOR gate using only NAND gates. (BTW, mostly all circuit problems assume you have two inputs plus 0 and 1 also as inputs).
Solution
You may be able to find the solution on the discussion forum.
Smart Cookie
Did you ever wonder how they make those pillsbury cookie dough rolls with the intricate faces inside them? Look here and notice the intricate design they have somehow injected into their cookie rolls? If you examine the roll closely there is no seam between the normal dough and the colored shape, but somehow they get that inside the roll. I emailed them asking them how they do it and they told me...
March 2010
9 posts
Wanna Play?
I offer to play a card game with you using a normal deck of 52 cards. the rules of the game are that we will turn over two cards at a time. if the cards are both black, they go into my pile. if they are both red, they go into your pile. if there is one red and one black, they go into the discard pile.
We repeat the two card flipping until we’ve gone through all 52 cards. whoever has...
Crazy Guy on the Airplane
A line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let’s say that the nth passenger in line has a ticket for the seat number n.)
Unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite...
Chameleons
At one point, a remote island’s population of chameleons was divided as follows:
13 red chameleons
15 green chameleons
17 blue chameleons
Each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.) is it ever possible for all chameleons to become the same color? why or why...
Railroad Bridge
A man needs to go through a train tunnel. He starts through the tunnel and when he gets 1/4 the way through the tunnel, he hears the train whistle behind him. you don’t know how far away the train is, or how fast it is going, (or how fast he is going). All you know is:
if the man turns around and runs back the way he came, he will just barely make it out of the tunnel alive before the...
Cars on the Road
if the probability of observing a car in 20 minutes on a highway is 609/625, what is the probability of observing a car in 5 minutes (assuming constant default probability)?
Solution
I haven’t written up a solution for this yet, but smarter people than I have described some on the discussion forum.
You can read their thoughts here.
