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

You are not logged in. #1 20130921 11:16:14
CombinatoricsThere are 2 types of red pens, 3 types of blue pens, and 4 types of green pens. 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #2 20130921 18:06:17
Re: Combinatorics
Let's say you have these colours red1, red2, blue1, blue2, blue3, green1, green2, green3, and green4. That's nine colour choices. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #3 20130921 19:32:34
Re: CombinatoricsHi Bob The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #4 20130921 20:47:47
Re: CombinatoricsMy first attempt at this question interpreted the problem differently. Then I deleted it and tried again. Now I'm not sure. We await Agnishom's clarification. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #5 20130921 20:54:09
Re: CombinatoricsI'd say the answer is 3 if samecoloured pens are the same and 72 if they are different. and Last edited by anonimnystefy (20130921 22:18:29) The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #6 20130921 22:13:06
Re: CombinatoricsI think they are different 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #7 20130921 22:19:05
Re: Combinatorics
So, it should be 2*3*4*6 = 144. But why is it 72? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #8 20130921 22:24:07
Re: CombinatoricsI already said that isn't correct. If you did it like that, you would count picking red1, red2, blue1, green1 and red2, red1, blue1, green1 as different picks, when they are truly the same. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #9 20130921 22:32:34
Re: CombinatoricsHi Agnishom The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #10 20130922 01:54:21
Re: Combinatorics
I am sorry, I could not follow. How is it coming to 72? 'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.' 'God exists because Mathematics is consistent, and the devil exists because we cannot prove it' 'Who are you to judge everything?' Alokananda #11 20130922 02:06:37
Re: CombinatoricsYou can do it by casework or using the GF above. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #13 20130922 02:35:59
Re: CombinatoricsI don't know how I would program this one, and it's a simple enough a problem that it doesn't need to be programmed. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #14 20130922 02:40:45
Re: CombinatoricsHmmm.
So then it is not so simple. DZ says you do not understand the problem until you program it. This always lends insight and satisfies the "two solution rule." In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #15 20130922 02:42:25
Re: CombinatoricsI have two solutions. Classic casework and the GF. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #16 20130922 02:47:08
Re: CombinatoricsAnd if the problem were say 20 pens and 16 to 1 types would you still want to casework it? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #17 20130922 02:53:49
Re: Combinatorics
What? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #18 20130922 02:58:57
Re: CombinatoricsWhat I am saying is casework is a very clumsy way of working sufficient for small problems only. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #19 20130922 03:12:39
Re: CombinatoricsI know, I dislike casework, too, but tend to use it if it seems possible. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #20 20130922 03:17:50
Re: CombinatoricsYes I did. But it refuses to get the answer I want. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #21 20130922 03:20:54
Re: CombinatoricsCan you post the code you currently have? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #22 20130922 03:24:55
Re: CombinatoricsCode:s = {{r, 1}, {r, 2}, {b, 1}, {b, 2}, {b, 3}, {g, 1}, {g, 2}, {g, 3}, {g, 4}}; ans = Permutations[s, {4}]; ans1 = Select[ans, Length[Union[#[[All, 1]]]] >= 3 &]; ans2 = Select[ans1, Length[Union[#[[All, 2]]]] == 4 &]; Union[Sort[#] & /@ ans2] This is the output In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #23 20130922 03:30:09
Re: CombinatoricsThe definition of ans2 is incorrect. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #24 20130922 03:33:29
Re: CombinatoricsWhat would you do from there? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #25 20130922 03:42:15
Re: CombinatoricsWhat did you try to do to get ans2, ie. what did you think Select[ans1, Length[Union[#[[All, 2]]]] == 4 &]; would do? The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment 