Sorry, 22. I needed to constrain the two systems. Too much linear algebra to want to explain, but yeah, Vandermonde and all that.
On Tue, Sep 9, 2025 at 9:22 PM Jon Zingale <[email protected]> wrote: > It's 29. > > I am assuming you are thinking of a polynomial that generates each > sequence. Unfortunately, it's a 6th degree polynomial and so solving for > the coefficients is a pain. You construct a Vandermonde matrix (V) a vector > of dummy coefficients a = [a0, a1, ..., a6]. Then you solve for the > coefficients relative to your sequence (S), V * a = S. > > Python helped nicely: > > import numpy as np > > n1 = np.array([0, 1, 2, 3, 4, 5, 6]) > y1 = np.array([1, 3, 5, 6, 8, 10, 12]) > coeffs1 = np.polyfit(n1, y1, 6) > sol1 = np.polyval(coeffs, 7) > > n2 = np.array([0, 1, 2, 3, 4, 5, 6]) > y2 = np.array([1, 3, 4, 6, 8, 9, 10]) > coeffs2 = np.polyfit(n2, y2, 6) > sol2 = np.polyval(coeffs, 7) > > =>29 > > > On Tue, Sep 9, 2025 at 3:17 PM Nicholas Thompson <[email protected]> > wrote: > >> Sry. Should be all commas. >> >> >> Sent from my Dumb Phone >> >> On Sep 9, 2025, at 1:19 PM, Nicholas Thompson <[email protected]> >> wrote: >> >> >> Here are two mathematical series >> >> 1,3,5,6,8,10.12, __ >> 1.3.4,6,8,9,10, __ >> >> Both have the same next number. >> Why, and what are we talking about here? >> >> I predict that only Jon will guess the answer. >> >> Please dont trouble yourself with this if you have anything better to do. >> >> >> >> Nick >> Nicholas S. Thompson >> Emeritus Professor of Psychology and Ethology >> Clark University >> [email protected] >> https://wordpress.clarku.edu/nthompson >> >
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