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You are not logged in. #8926 20130309 19:34:20
Re: Linear Interpolation FP1 FormulaWe sent 8 emails to each other yesterday. I'll find out where she lives... maybe we can walk to school together. #8927 20130309 19:38:16
Re: Linear Interpolation FP1 FormulaI am coming up with 70 such numbers for 4 digits alone. 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. #8928 20130309 19:41:24
Re: Linear Interpolation FP1 FormulaSorry, should have specified, the number has to be 4digits long, so 70 is the right answer. How did you do it with GFs? #8929 20130309 19:44:27
Re: Linear Interpolation FP1 FormulaThe answer is the coefficient of x^0, which is 70. Last edited by bobbym (20130309 19:49:38) 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. #8930 20130309 19:54:20
Re: Linear Interpolation FP1 FormulaI can see that the second bracket represents the 1s, but what is happening in the others? #8931 20130309 19:55:44
Re: Linear Interpolation FP1 FormulaThe first bracket represents the first digit. It can be from 1 to 4. 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. #8932 20130309 19:59:06
Re: Linear Interpolation FP1 FormulaOkay, that makes sense... but I don't understand why you have negative exponents for the last two. Why isn't it just the second bracket cubed since each of the other numbers can be from 0 to 4? #8933 20130309 20:04:00
Re: Linear Interpolation FP1 FormulaWhen you are solving a problem like this you are really solving a linear diophantine equation. Mathematics consists of taking a problem that is in one form and changing into another that has the same number of solutions. One that we can solve. We will get into the "teakettle principle" in just a minute. Last edited by bobbym (20130309 20:04:32) 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. #8934 20130309 20:11:42
Re: Linear Interpolation FP1 FormulaOh, I see... so it becomes #8935 20130309 20:17:31
Re: Linear Interpolation FP1 FormulaThat is one way of looking at it. The last two brackets just represent c and d taking on values of 4 to 0. We see the constant coefficient ( x^0 ) is 70. What do you think the 34 x^4 tells us? 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. #8936 20130309 20:21:03
Re: Linear Interpolation FP1 FormulaThe number of solutions to a + b + c + d = 4? #8937 20130309 20:25:55
Re: Linear Interpolation FP1 FormulaYes! It means that there are 34 ways to write that 4 digit number abcd such that a + b is 4 greater than c + d. 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. #8938 20130309 20:27:58
Re: Linear Interpolation FP1 FormulaAh, I see. Thanks for the solution! Now on to the second part of the question. #8939 20130309 20:33:25
Re: Linear Interpolation FP1 FormulaWhat second part? 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. #8940 20130309 20:50:05
Re: Linear Interpolation FP1 FormulaIt asks for how many 4digit numbers can be made using the numbers 0 to k. I used the same approach, it did not work... #8941 20130309 21:01:22
Re: Linear Interpolation FP1 FormulaHi; 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. #8942 20130309 21:08:51
Re: Linear Interpolation FP1 FormulaYes, that's the one  although, this question is from a public exam paper where only a pen is allowed... #8943 20130309 21:16:02
Re: Linear Interpolation FP1 FormulaYes, but the important part is that we have the answer... Do they agree that is correct? 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. #8944 20130309 21:17:33
Re: Linear Interpolation FP1 FormulaYes. It is okay, I found the 'full solution'  although, I am trying to see if I can do it with a GF. #8945 20130309 21:20:51
Re: Linear Interpolation FP1 FormulaCan you supply the link? 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. #8946 20130309 21:22:22#8947 20130309 21:25:14
Re: Linear Interpolation FP1 FormulaTo both if you have them. In case I do not get 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. #8948 20130309 21:29:23
Re: Linear Interpolation FP1 Formulaw w w . m a t h s h e l p e r . c o . u k / o x b . h t m #8949 20130309 21:29:57#8950 20130309 21:34:45
Re: Linear Interpolation FP1 FormulaSorry, it did not work. Looking at a gf approach. 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. 