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

You are not logged in. #1 20120520 21:30:00
The Wrong Hats ProblemIt has been many days since I last posted. Feeling to post again '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 20120520 21:41:21
Re: The Wrong Hats ProblemHi; 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. #3 20120520 21:47:48
Re: The Wrong Hats ProblemHow do you get it? '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 #4 20120520 21:49:32
Re: The Wrong Hats ProblemIf I am correct,than this is the derangement problem for 8 elements. I think you can find it on Wikipedia. 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 #5 20120520 21:51:26
Re: The Wrong Hats ProblemYes, this is a derangement problem. You can first use the approximation of There are many formulas to generate the number of derangements. http://en.wikipedia.org/wiki/Derangement 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. #6 20120520 21:58:22
Re: The Wrong Hats ProblemThnks I will read the article but will you explain what is approximation of 1/e? '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 20120520 21:59:19
Re: The Wrong Hats ProblemAs n approaches infinity the probability of a derangement approaches 1 / e. 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. #8 20120520 22:10:15
Re: The Wrong Hats Problemhttp://upload.wikimedia.org/wikipedia/en/math/3/f/6/3f619a61786028a59a524136391f52f0.png '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 #9 20120520 22:17:02
Re: The Wrong Hats ProblemHi; 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. #10 20120520 22:20:24
Re: The Wrong Hats ProblemHi bobbym Last edited by anonimnystefy (20120520 22:20:43) 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 #11 20120520 22:21:22
Re: The Wrong Hats ProblemThe formula is: Last edited by Agnishom (20120520 22:21:58) '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 #12 20120520 22:25:28
Re: The Wrong Hats ProblemHi Agnishom; 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. #13 20120520 22:34:12
Re: The Wrong Hats Problem
Now would you please explain point 1 and 2 '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 #14 20120520 22:38:55
Re: The Wrong Hats ProblemHi Agnishom; 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 20120520 22:46:04
Re: The Wrong Hats ProblemDear Bobbym, '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 #16 20120520 22:49:05
Re: The Wrong Hats ProblemHi; 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 20120625 12:32:09
Re: The Wrong Hats ProblemActually I don't understand these two lines: '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 #18 20120625 12:46:30
Re: The Wrong Hats ProblemYou could've said that we start from Person 2 for the casework, but that wouldn't change much except a few indexes. The point of that casework is to see what are the values weget for each case that exists. 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 #19 20120628 14:43:01
Re: The Wrong Hats ProblemActually I still don't get it '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 #20 20120705 19:20:23
Re: The Wrong Hats Problem
I would have thought the answer was simply 7/8*6/7*5/6*4/5*.3/4*2/3*1/2*1/1=3/4 #21 20120705 20:36:48
Re: The Wrong Hats ProblemHi biffboy; 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. #22 20120710 11:48:55
Re: The Wrong Hats ProblemHi biffboy '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 #23 20120710 12:07:18
Re: The Wrong Hats ProblemHi 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 #24 20120710 18:48:00
Re: The Wrong Hats ProblemHi Agnishom; 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. 