Challenge: sum of squares. Let's break 299
01-21-2018, 05:41 AM (This post was last modified: 01-21-2018 03:02 PM by Thomas Okken.)
Post: #20
 Thomas Okken Senior Member Posts: 1,090 Joined: Feb 2014
RE: Challenge: sum of squares. Let's break 299
I let my code run for over twelve hours, by which time it had gotten to 82.
Here's how the CPU time use progressed, in a log plot, N vs CPU time in seconds:

[attachment=5580]

It does indeed look exponential, as expected. I fed the data to Free42 STAT, removing the times of 0.000 seconds, and got an exponential fit with a correlation coefficient of 0.96 and an exponent of 0.281. Extrapolated run time for N=300: 4.78e22 years.

The connectedness of the graph of pairs of numbers that sum to squares grows pretty slowly. When you add N to the graph for 1 through N-1, the number of edges added is floor(sqrt(2n-1)) - ceil(sqrt(n+1)) + 1, so, asymptotically, each successive N adds (sqrt(2)-1)*sqrt(N) edges. That's slow, but still fast enough that dumb backtracking isn't useful.
 « Next Oldest | Next Newest »

 Messages In This Thread Challenge: sum of squares. Let's break 299 - pier4r - 01-18-2018, 09:32 PM RE: Challenge: sum of squares. Let's break 299 - TheKaneB - 01-18-2018, 10:58 PM RE: Challenge: sum of squares. Let's break 299 - Didier Lachieze - 01-19-2018, 12:08 AM RE: Challenge: sum of squares. Let's break 299 - Didier Lachieze - 01-19-2018, 12:15 PM RE: Challenge: sum of squares. Let's break 299 - Paul Dale - 01-19-2018, 04:29 AM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-20-2018, 05:43 PM RE: Challenge: sum of squares. Let's break 299 - John Keith - 01-20-2018, 08:19 PM RE: Challenge: sum of squares. Let's break 299 - Paul Dale - 01-20-2018, 10:13 PM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-20-2018, 10:31 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 02:17 AM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-19-2018, 04:29 AM RE: Challenge: sum of squares. Let's break 299 - Paul Dale - 01-19-2018, 06:31 AM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-19-2018, 06:48 AM RE: Challenge: sum of squares. Let's break 299 - pier4r - 01-19-2018, 12:40 PM RE: Challenge: sum of squares. Let's break 299 - Didier Lachieze - 01-19-2018, 12:47 PM RE: Challenge: sum of squares. Let's break 299 - Didier Lachieze - 01-19-2018, 04:26 PM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-19-2018, 04:33 PM RE: Challenge: sum of squares. Let's break 299 - Didier Lachieze - 01-19-2018, 04:56 PM RE: Challenge: sum of squares. Let's break 299 - ggauny@live.fr - 01-20-2018, 06:15 PM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-20-2018, 09:08 PM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-21-2018 05:41 AM RE: Challenge: sum of squares. Let's break 299 - Gilles59 - 01-21-2018, 10:44 PM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-22-2018, 01:40 AM RE: Challenge: sum of squares. Let's break 299 - TheKaneB - 01-22-2018, 11:54 AM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-22-2018, 01:11 PM RE: Challenge: sum of squares. Let's break 299 - TheKaneB - 01-22-2018, 03:19 PM RE: Challenge: sum of squares. Let's break 299 - Gilles59 - 01-22-2018, 08:49 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-24-2018, 09:18 PM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-24-2018, 09:43 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-24-2018, 10:03 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-24-2018, 10:08 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-24-2018, 10:14 PM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-24-2018, 10:16 PM RE: Challenge: sum of squares. Let's break 299 - TheKaneB - 01-24-2018, 10:22 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-24-2018, 10:29 PM RE: Challenge: sum of squares. Let's break 299 - pier4r - 01-25-2018, 05:54 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-24-2018, 10:32 PM RE: Challenge: sum of squares. Let's break 299 - Thomas Okken - 01-24-2018, 10:33 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 01:47 AM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 01:49 AM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 01:55 AM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 02:04 AM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 03:25 AM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 04:19 AM RE: Challenge: sum of squares. Let's break 299 - TheKaneB - 01-25-2018, 09:33 AM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 10:53 AM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-25-2018, 11:10 PM RE: Challenge: sum of squares. Let's break 299 - TheKaneB - 01-26-2018, 12:29 AM RE: Challenge: sum of squares. Let's break 299 - pier4r - 01-26-2018, 08:15 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-26-2018, 10:01 PM RE: Challenge: sum of squares. Let's break 299 - pier4r - 01-27-2018, 01:23 PM RE: Challenge: sum of squares. Let's break 299 - Massimo Gnerucci - 01-27-2018, 02:14 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 01-28-2018, 04:14 PM RE: Challenge: sum of squares. Let's break 299 - brickviking - 01-29-2018, 07:13 PM RE: Challenge: sum of squares. Let's break 299 - peacecalc - 01-30-2018, 02:51 PM RE: Challenge: sum of squares. Let's break 299 - Allen - 02-01-2018, 03:38 AM RE: Challenge: sum of squares. Let's break 299 - Allen - 02-01-2018, 03:40 AM RE: Challenge: sum of squares. Let's break 299 - TheKaneB - 02-01-2018, 10:54 AM

User(s) browsing this thread: 1 Guest(s)