almostbusto
04-16-2007, 07:38 PM
Well I am sure this math problem has been solved, its not very difficult, but i can't find it published anywhere. I want to compare the standard published solution to mine just to see how ugly mine is.
anyway here's the problem:
every math nerds knows that given a sequence like 1, 2, 3, 4.... or 1, 4, 9, 16... that the next number can actually be any real number. meaning that there is a function that maps the first five positive integers to 1, 2, 3, 4, X where X is any real.
so I was thinking about IQ tests which always seem to ask about the next number in a sequence and how idiotic that is. I quickly decided that a better question is to ask for a function that maps the first N positive integers to N given numbers. Eventually i decided that might not be a good question either if there was an algorithmic solution that could be executed for any sequence. I was sure there was such an algorithm.
a bit later i am in the shower and going over this again and i come up with an algortihm that will map the first N integers to any possible sequence of real numbers of length N. you give me the sequence you want, ill give you the function.
so its not that hard of a problem, feel free to post your solutions in this thread.
edit: found this link http://qntm.org/1111 which seems to have a method. his method is prettier in some ways. i always knew that a nth degree polynomial can be made to pass through any N points. This is something they cover in first year regression (a regression with N data points and N regressors will always have perfect fit). however, a person taking an IQ test can't just solve N simultaneous equations instantly. my solution is instant, you give me the numbers and then i can immediately start writing the solution.
EDIT2: a second similar link http://mathforum.org/library/drmath/view/56864.html
anyway here's the problem:
every math nerds knows that given a sequence like 1, 2, 3, 4.... or 1, 4, 9, 16... that the next number can actually be any real number. meaning that there is a function that maps the first five positive integers to 1, 2, 3, 4, X where X is any real.
so I was thinking about IQ tests which always seem to ask about the next number in a sequence and how idiotic that is. I quickly decided that a better question is to ask for a function that maps the first N positive integers to N given numbers. Eventually i decided that might not be a good question either if there was an algorithmic solution that could be executed for any sequence. I was sure there was such an algorithm.
a bit later i am in the shower and going over this again and i come up with an algortihm that will map the first N integers to any possible sequence of real numbers of length N. you give me the sequence you want, ill give you the function.
so its not that hard of a problem, feel free to post your solutions in this thread.
edit: found this link http://qntm.org/1111 which seems to have a method. his method is prettier in some ways. i always knew that a nth degree polynomial can be made to pass through any N points. This is something they cover in first year regression (a regression with N data points and N regressors will always have perfect fit). however, a person taking an IQ test can't just solve N simultaneous equations instantly. my solution is instant, you give me the numbers and then i can immediately start writing the solution.
EDIT2: a second similar link http://mathforum.org/library/drmath/view/56864.html