Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20060907 23:37:10
Battleship on the number lineThere is a battleship on the number line with position x at time t, with x always an integer when t is an integer. Bad speling makes me [sic] #2 20060908 01:10:08
Re: Battleship on the number lineAre we told what the constant speed is that the battleship is travelling at? If we're not, then I don't think it's possible. Maybe it's not even if we are. Or maybe I'm just not thinking hard enough. Maybe I'm saying maybe too much. Why did the vector cross the road? It wanted to be normal. #3 20060908 02:56:04
Re: Battleship on the number lineWe are not told the speed the battleship is traveling at, nor where it starts, nor which direction it is going... but I assure you, there is a way to do it Bad speling makes me [sic] #4 20060908 22:38:49
Re: Battleship on the number linewhat kind of battleship and of which nationality tell me and I will tell you the answer. Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized. #5 20060909 00:56:49
Re: Battleship on the number lineI believe it is impossible. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #6 20060909 01:49:58
Re: Battleship on the number line
You are quite close to hitting the nail on the head here! I assure you it is entirely possible, I wouldn't want to infuriate anybody by wasting their time... you just have to be a little creative (though I don't mean bending the rules  it's not a word puzzle) Bad speling makes me [sic] #7 20060910 03:36:47
Re: Battleship on the number lineI think it's impossible too unless two ends of the line joins each other straightly . #8 20060910 11:00:16
Re: Battleship on the number lineFunny, I've never seen the end of the number line. What does it look like? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #9 20060910 11:14:00
Re: Battleship on the number lineWell, it looks more like a circle around the Earth on which the battleship is moving away from its starting point. Last edited by tt (20060910 11:17:03) #10 20060910 13:35:23
Re: Battleship on the number lineIf it has the Earth involved, suppose the Earth is absolutely round and the number line is a straight line, you can ignite the bomb at the point of contact when t=0 before the battleship sailing off into space. #11 20060910 14:02:19
Re: Battleship on the number linett, the problem mentions nothing about the earth. We are on the number line. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #13 20060911 22:31:15
Re: Battleship on the number lineit is going southwest to the falklands at 100 knots. Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized. #14 20060911 23:29:34
Re: Battleship on the number lineHere's my thinking: Why did the vector cross the road? It wanted to be normal. #15 20060912 02:29:19
Re: Battleship on the number line
Don't forget you'd need to cover all the negative numbers as well.
What I think you're saying is that if your algorighm has a certain fixed speed (or rate of coverage of the integers) then it is possible for the ship to travel faster than this fixed speed, so it can never garuntee hitting the ship.... more on this later, but more than one hint for now would be far too generous. Bad speling makes me [sic] #16 20060912 09:37:29
Re: Battleship on the number lineAs an aside, you can make a very minor variation to this algorithm so that it will work for a ship whose starting point and speed are any rational number, but you cannot do it for a ship whose starting point and speed are any real number. Bad speling makes me [sic] #17 20060912 10:20:49
Re: Battleship on the number lineI realised that it would need to cover all the negative numbers, but since 0 to infinity is an infinity of numbers, then if the algorithm works for that range then it must also work for the infinity to infinity. And 0, 1, 2, 3 is easier to write than ∞, ∞+1, ∞+2 etc. Why did the vector cross the road? It wanted to be normal. #18 20060912 22:23:21
Re: Battleship on the number lineno the ship is my personal clipper and is flying northeast to mars. Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized. #19 20060912 22:47:53
Re: Battleship on the number line
Now all you have to do is point out where mars is on the number line and you've got your answer Bad speling makes me [sic] #20 20060913 22:19:32
Re: Battleship on the number line46427. is where it is on the number line, i win. Chaos is found in greatest abundance wherever order is being saught. It always defeats order, because it is better organized. #21 20060914 10:52:38
Re: Battleship on the number lineIs anyone still trying to solve this? Or can we ask for the solution? "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #22 20060915 05:35:21
Re: Battleship on the number lineWell, for anyone still trying to figure it out, here is a really big hint: And if you just want to know the solution (I told you there was one!)  here it is: Last edited by Dross (20060915 08:47:26) Bad speling makes me [sic] #23 20060916 05:46:12
Re: Battleship on the number lineBut surely... Why did the vector cross the road? It wanted to be normal. #24 20060916 10:14:25
Re: Battleship on the number line
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #25 20060916 10:20:24
Re: Battleship on the number lineNow, let's make things interesting: "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." 