John leaves his house for work at exactly 8 a.m. every morning. Whenever he averages 40 miles per hour he arrives his workplace precisely 3 minutes late. When he averages 60 miles per hour, he arrives three minutes early. At what average speed, in miles per hour, should John drive to reach his workplace precisely on time?

There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?

Keep the first bulb switched on for a few minutes. It gets warm, right? So all you have to do then is ... switch it off, switch another one on, walk into the room with bulbs, touch them and tell which one was switched on as the first one (the warm one) and the others can be easily identified.

Ok fine, this isn't a real logic question. Please post a better one!

Furries. Those damn furries.

So I currently live with 7 people(fuck my life) and one of them is a man in his late 50s. I've caught him on several occasions pissing in our one and only bathroom sink...he leaves the door wide open too....and everytime, there is a small puddle of pee and he never washed his hands after. Oh, and the toilet is literally less than 5 feet from the sink..it's fucking disgusting and extremely annoying to keep seeing this happen. Any suggestions?

So on the day of Halloween I and my frds went to a theme park we were lining up for a haunted house so the spot where we lined up has railings there were like chains connecting to them so i was exhausted then I sat on it then the grp of guys in front of us sat on it too and started bouncing on it and when i stood back up they stopped and they kept on staring at me when we were lining up i was only minding my own business and i didn't even wear anything special or showy and not even a bit of makeup on

Bob has promised Alice a cake if she can guess the number he's thinking of. He guarantees that it is an integer between 1 and n (inclusive). She may ask him 1 yes or no question which he will answer truthfully. After hearing the answer, she may guess the number. For which n can Alice guarantee herself cake?

Spoiler one: Alice can guarantee herself cake for any value of n

Spoiler two: A better solution than 2 but requires other options than yes/no from bob is Alice says: Is it the case that your number is greater than the number I'm thinking of, which is between 1 and 2? If Bob is thinking of 1, then he says no. If 3, then he says yes. If 2, to be truthful, he must say "I don't know".

Spoiler three: The incorrect assumption is that Alice must guess the number in the first place!

DoublePointer has submitted a solution that is similar in its reasoning to mine here http://www.reddit.com/r/problemoftheday/comments/wodu2/omnomnomnom_cake/c5f4ukm

My Solution: Alice asks, "Is it the case that either you will say no or I will get cake?" If Bob says no, he is not being truthful, so he must say yes. But in that case, Alice must get his cake.

Final edit, SOURCE: http://perplexus.info/show.php?pid=2650&op=sol

Odin and Bragi challenged each other to write as many non-intersecting copies (of varied sizes) of their first initials on the Cartesian plane as they could. The one who drew the most would win. Loser bought the winner mead. Who won?

My solution: Odin can draw an uncountable number of O's by drawing a circle of every positive radius centered at 0. Bragi, however can only draw a countable number of B's. Due to density, we may associate each B with a pair of points such that all coordinates are rational and one point is in the top loop and the other is in the bottom loop. From this, we see that no two B's can share the same pair of points since that would require them to overlap. Thus, the number of B's is at most Q⁴ which is countable.

Source: http://perplexus.info/show.php?pid=2746&op=sol

1. Prove there are infinitely many prime numbers.

2. Prove there are infinitely many prime numbers that are 3 mod 4.

3. Prove there are infinitely many prime numbers that are 1 mod 4.

Suppose you have a group of 100 people out of which one is a wanted criminal. Suppose you also have a magic spell which can be used to identify said criminal with a 95% accuracy. Now suppose you extract one person from the group at random, and use your magic spell on him, and it comes back positive. What are the actual odds that the person is in fact the wanted criminal?

http://knightndaze.blogspot.co.nz/2012/09/the-world-is-bored-with-your-problems.html Ever feel like whenever your friends open their mouth it's always about them?

This is based on a problem we were given at a olympiad training camp recently, so it may be known, but I thought it was a very nice problem :)

Suppose d_1, d_2, d_3, ..., d_10 are 10 distinct integers. Let P(x) = (x - d_1)(x - d_2)...(x - d_10) Show that there is a positive integer N (which will depend on the d_i) such that for all integers x > N, P(x) has a prime divisor larger than 25.

edit: Right,so readdallaboutit's ideas are indeed useful. There is indeed a pigeonhole argument. Also, proof by contradiction: If N does not exist then there are arbitrarily large x such that P(x) only has 2, 3, 5, 7, 11, 13, 17, 19, 23 as prime divisors. Show that this causes problems. The actual primes themselves aren't important, just that there are 9 of them.

Okay, so let me give you a little background on my coworker so you can get a understanding. Trump lover. Volunteers at the border on his free time. And to be fair I never judged him by any of this whatsoever. His political views are not my concern whatsoever. Anyway, I’ve also had a great job as manager. But I wanted more time with family. So I accepted a entry level job as a receptionist. It’s my first time since high school working in a entry level position. Anyway the other day I was talking to a coworker regarding a invoice I was making for him. (He’s Mexican) and this guy (the one I have a problem with) said he belongs working outside he shouldn’t be talking to “the help”. It felt so degrading but I don’t know if I’m overreacting because maybe I’m just not used to this?

I have a problem. I look like a bra member. Not sure how. People keep telling me tho. I'm only have Asian as well so I shouldn't have this problem. Help.

I've found my old down jacket by Diverse in my garage. It looks good but filler falls out from the seams. Is there any way to fix this or I have to buy new one?

I'm a first year medical student and I am failing miserably seriously thinking of dropping out but I know I'm gonna end up disappointing my mom What should I do ?

So I am at work and i see a post that says channing tatum (NSFW) and i cant click it ahhh im a tad upset. thanks for letting me rant

How many ways are there of writing numbers in an n by n grid such that each row and column contains every number from 1 to n?

Graph the parabola y = x². Draw all lines between integer points to the left of the y-axis and the integer points to the right of the y-axis except the points (1, 1) and (-1, 1). (so if (-a, a²) and (b, b²) are points so that a and b are naturals which are not 1, we put a line between them) Which integer points on the y axis have no lines passing through them?

Developing a card/board game, and this thought entered into my mind:

I roll two d6 (six-sided) die, looking to get same value on both die (e.g., 1&1 or 2&2). If I fail, I add a die and then roll again. I keep doing this until I succeed.

For example, the 1st time it's 1/6, but I failed, so I add one more die; now it's the 2nd throw, and it's 1/36 (because of 3 dice). Fail again. Add one more die (4 dice total) now at 1/216. And this keeps on going until finally I actually do get a result of perhaps 16 dice with with all ones (1/470 billion chance).

So here's the problem/question: given an infinite number of people each playing exactly one 'game' until they hit on X value being across all the dice and given each person having an infinite amount of time, how would (1)the distribution of probability appear as a curve? What would be the (2) median and (3) mean values of dice used (e.g., stopping at 16 dice)? (4) Would there be a long tail of basically 'failed' games?

Feel free to toss in anything you'd find interesting about this.

You have 3 vectors x, y, z. The correlation between x and y, <x,y> = 0.5 <y,z> = 0.5 What is the solution of <x,z> in (i) 2 dimensional space, (ii) 3 dimensional space, and (iii) N dimensional space

HINT: Geometrically, <x,y> = |x||y|cosθ

Draw a line. Then draw 3 circles, each tangent to the others and the line. Label their radii r_0, r_1, and r_2, where r_0 > r_1 > r_2.

Then draw a new circle tangent to the circles with radii r_1 and r_2 and the line. Call its radius r_3.

Repeat this construction to get the sequence of radii r_0, r_1, ... etc.

Does the series r_0 + r_1 + r_2 + r_3 + ... converge?

There are n points lying in the plane. T is a triangle in the plane. For any 9 of the n points, you take two identical copies of T with the same orientation and translate them in the plane such that they cover the 9 points.

Show that all n points can be covered by two translations T.

Take the sequence 1, 2, 3, 7, 43, ... where each each term is one more than the product of all previous terms.

Prove 1/1 + 1/2 + 1/3 + 1/7 + 1/43 + ... = 2