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Everything posted by EventHorizon

Arrangement, Again and Again
EventHorizon replied to EventHorizon's question in New Logic/Math Puzzles

Inspired by I thought I would give my own. 2,4,3,1,6,5,7 3,7,5,6,1,8,2,4 2,7,6,3,9,4,8,5,1 1) What would it be for 10 numbers? What method am I using? Here's another one (but it is (hopefully) harder, so I'll give all of them up to 9): 1 1,2 1,2,3 4,1,3,2 3,1,4,5,2 6,3,2,5,4,1 1,4,3,2,6,5,7 5,7,8,6,4,1,3,2 4,5,8,6,2,7,3,1,9 2) What is the order for 10 numbers? What is the method?

All the people like us are We, and everyone else is They.
EventHorizon replied to bonanova's question in New Logic/Math Puzzles
And another excerpt from the page for "0.999..." So since decimal places are the digits after the decimal point, it seems there is one pair of equal decimal expansion representations for each positive integer and each negative integer. And this is exactly the set of all the numbers that fit the OP. Any other terminating decimal expansion will have the pair of representations equal at one or more decimal places. It is interesting that 0 fails in this regard. The method of decimal representation we use has no way of approaching 0 with repeating 9's due to the fact that adding value i 
Interesting one  A Cat and A mouse
EventHorizon replied to ujjagrawal's question in New Logic/Math Puzzles

Interesting one  A Cat and A mouse
EventHorizon replied to ujjagrawal's question in New Logic/Math Puzzles
I found a mistake in the derivation, so my equation is wrong. I accidently omitted something which made it much easier to solve, but incorrect. 
Interesting one  A Cat and A mouse
EventHorizon replied to ujjagrawal's question in New Logic/Math Puzzles
(Hint: don't look for the curve, just examine the distance between them and how it changes with time) I'll try (again) to find the equation for the path in a bit. Edit: I thought I'd include the last equation I got, but kept failing to verify. So I don't know it if is correct. 
Voyage to The Bottom of the Earth [and back]
EventHorizon replied to bonanova's question in New Logic/Math Puzzles

Voyage to The Bottom of the Earth [and back]
EventHorizon replied to bonanova's question in New Logic/Math Puzzles
So now we just need to determine if it matters if the frictionless tunnel goes through the center of the earth or not. 
Yes or No? I really don't know!
EventHorizon replied to bonanova's question in New Logic/Math Puzzles

Yes or No? I really don't know!
EventHorizon replied to bonanova's question in New Logic/Math Puzzles

Voyage to The Bottom of the Earth [and back]
EventHorizon replied to bonanova's question in New Logic/Math Puzzles

Voyage to The Bottom of the Earth [and back]
EventHorizon replied to bonanova's question in New Logic/Math Puzzles
This means that you can completely ignore the parts of the earth further than you from the center of the earth, so effectively you feel the gravity of standing on a smaller earth. The effective mass of this smaller earth would be d*(4/3)pi*r2^3, where d is the density of the earth (assumed in the OP as homogeneous) and r2 is your distance from the center of the earth. Notice that this effective mass is equal to the mass of the earth multiplied by r2^3/r^3. Plugging the new mass and radius into the equation to calculate gravitation gives f2 = GmE(r2^3/r^3)/r2^2 = (r2/r)*GmE/r^2 = (r2/r) 

So it looks like I had paradoxes on the mind when drafting that post. What I meant (in each of the three mentions of the word paradox) was contradiction. I hate when I read through one of my posts and find misused words. Too bad I'm no longer a VIP or I'd be able to fix them. Edit: Hey, I'm a VIP again, thanks rookie1ja.

Didn't notice psykomakia's post. That's what i get for making dinner while puzzling.

Edit: Fixed terminology.

Can u help prisoners to get free ?
EventHorizon replied to ujjagrawal's question in New Logic/Math Puzzles

Third, fold again using a fanlike method as shown in the diagram below, alternating forwards and backwards folds. Now all the perforation and only the perforation is along that diagonal... so letta rip.

If you cannot assume...


Touring the chessboard with a single die
EventHorizon replied to bonanova's question in New Logic/Math Puzzles
#include <stdio.h> #include <stdlib.h> #include <iostream> #include <memory.h> #include <vector> using namespace std; #define GRIDSIZE 8 enum dir { dir_front = 0, dir_back = 1, dir_up = 2, dir_down = 3, dir_right = 4, dir_left = 5, num_dirs = 6, dir_error = 7, dir_undo = 8 }; dir facing; dir move; vector<int> hist; int displacement = {0,0,GRIDSIZE,GRIDSIZE,1,1,0,0}; int startpos; dir startdir; dir tiltarray[] = {dir_error,dir_error,dir_up,dir_down,dir_right,dir_left, dir_error,dir_error,dir_down,dir_up,d 
Touring the chessboard with a single die
EventHorizon replied to bonanova's question in New Logic/Math Puzzles
Yeah, it would be easy. So easy in fact... that here it is Found one! _________________ 1 v=v=v=v=v=v=v XX X X X X X v 6=< v=v=v >=6 X XXX XXX  6 6=< 6=< 6 >=6 XX X XXX X ^=^ >=6=< ^=^=^  X XX X X X X  v=v >=6=< v=v=v XX X XXX X 6 6=< 6=< 6 >=6 X XXX XXX  ^ 6=< ^=^=^ >=6 XX X X X X X 1 ^=^=^=^=^=^=^  Found one! _________________ 1 v=v=v=v=v=v=v XX X X X X X v 6 6=<=1 >=6 6 XXX X XXX 6 ^=^ 6=< > ^=^ X X XXX