Question

Anyone have any fun problems? No easy stuff unless it's like super cute. ;P

Answer 1

yes go to my questions list and check out the second thread from the top if you haven't already

also here's a list of problems on rotation http://imgur.com/a/obPvf

Answer 2

U can try this-
Prove that the number of 5 tuples of positive integers (l,m,n,o,p) satisfying the equation

\[lmnop=5(lmno+mnop+nopl+oplm+plmn)\]is an odd integer

Answer 3

well this one interest me

https://www.youtube.com/watch?v=lA6hE7NFIK0

Answer 4

@imqwerty first thing I'm trying is this:

\[1=5( \frac{1}{l}+\frac{1}{m}+\cdots)\]

@Halmos I'm watching it now!

@ParthKohli I dunno, I don't feel particularly inspired by any of these problems right now unless you pick one heh

Answer 5

oh i have to go now i have list of good one, cya <3

Answer 6

Cool later

Answer 7

At noon a rocketship passes the earth with a velocity 0.8c. Observers on the ship and on earth agree that it is noon. At 12:30 pm as read by rocketship clock, the ship passes an interplanetary station that is fixed relative to the earth and whose clock reads earth time. What time is it at the station?

Answer 8

Not really sure I'm applying this formula correctly just looked it up:

\[12:00+\frac{30 }{\sqrt{1-.8^2}} \text{min}\]

Answer 9

\[\huge \color{red} \checkmark\]

Answer 10

@imqwerty is 0 considered a positive integer, I never know these things xD

Answer 11

I guess it'll work itself out anyways, since any value being zero implies all the rest are zero so it can only be that 0 contributes one tuple to the total answers.

Answer 12

Also uhhhh I don't really wanna work on these alone while you watch that's weird and boring please help I have no clue how to proceed hahaa xD

Answer 13

How far from earth is the station

Answer 14

can I take that time above, multiply it by .8c and get the distance?

Answer 15

Well, duh of course I can't what am I thinking lol

Answer 16

Here's one lol may not be so hard but its something

Answer 17

^ thats your hw problem, and you can empty dempty

Answer 18

haha its not homework

Answer 19

If you can tell me what's cute about it, I'll consider it

Answer 20

I guess it's kinda cute

Answer 21

lol @ empty

Answer 22

Ok since now you got that part how about at 12:30 pm rocketship time the ship reports by a radio back to earth, when by earth time does the earth receive the signal?

Answer 23

I don't know all these physics stuff I feel like I would just be looking up formulas to plug into, I want only math problems that I can work out here and now, plus I wanna finish qwerty's mabob lol

Answer 24

t=d/c

Answer 25

lol the investment one is a thinker but fun

Answer 26

we have to show that the number of solutions to\[\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}d + \frac{1}{e}=\frac{1}{5}\]is in the form \(2k + 1\).

Case 1: if all are equal, then there is only one such 5-tuple.
Case 2: if four are equal, then it can be shown that there are two solutions to this (21, 105) and (22, 55) so ten tuples.
Case 3: if three are equal, and two are unequal, then there are 5P2 = 5!/3! = 20 ways to reorganise each solution.
Case 4: if two are equal, and three are unequal, then there are 5P3 = 5!/2! = 60 ways to reorganise each solution.
Case 5: if all are unequal, then are are just 5! = 120 ways to reorganise each solution.

Therefore the number of tuples should be odd.

Answer 27

Solved the investment one:

\[x+y=a\]\[.035x+.06y=b\]
invert the matrix and left multiply to solve for x and y, done!

Answer 28

Nice @ParthKohli

Answer 29

*l,m,n..
:) yes thats correct @ParthKohli

Answer 30

how do the variables matter