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 Showing results 1 to 12 of 12 Search took 0.01 seconds. Search: Posts Made By: 0scar
 Forum: Puzzles 2020-09-12, 03:25 Replies: 26 Views: 2,060 Posted By 0scar I didn't know the chosen "cycle notation" too, I... I didn't know the chosen "cycle notation" too, I always used the "one-line notation" described by SmartMersenne. Wikipedia has an useful paragraph about them...
 Forum: Puzzles 2020-08-28, 14:28 Replies: 6 Views: 1,510 Posted By 0scar Spin-off solution The target sequence G(n) = F(n)*F(n+1) satisfies an order-3 homogeneous linear recurrence: G(n) = 2*G(n-1) + 2*G(n-2) - G(n-3), so we need a homogeneous linear system of order at least three to...
 Forum: Puzzles 2020-07-30, 05:57 Replies: 6 Views: 1,510 Posted By 0scar As LENGTH(n) grows exponentially, I think that it... As LENGTH(n) grows exponentially, I think that it makes sense to compute the ratios for n up to 10, or their limits as n grows to infinity (only for the brave) For my currently best solution, IBM...
 Forum: Puzzles 2020-07-30, 05:33 Replies: 6 Views: 1,510 Posted By 0scar Spin-off A friend of mine suggested a nice "spin-off" puzzle. If you solved July 2020 main problem by using three letters or more, and your dictionary includes letters "I", "B", and "M", then how many...
 Forum: Puzzles 2020-04-24, 05:46 Replies: 1 Views: 1,608 Posted By 0scar What about tiling an infinite board? Asymptotically, leave a fraction r of empty squares, and place each symbol in 1/3 of the remaining squares; ensure winning chance for no player. Can you do so for some explicit fraction r>0? Can...
 Forum: Puzzles 2020-04-14, 17:30 Replies: 44 Views: 5,762 Posted By 0scar I think that someone didn't stop on day 10 or on... I think that someone didn't stop on day 10 or on day 19, but he always checked every t until p >=.7 was reached. And he eventually found some p very, very close. My guess: somewhere before day 81.
 Forum: Puzzles 2020-04-13, 09:07 Replies: 44 Views: 5,762 Posted By 0scar On day 2, city B, only the 9000 people still... On day 2, city B, only the 9000 people still healthy can be infected (from A only): 1000+9000*0.1= 1900. Otherwise, some people infected on previous days are counted over and over again, quickly...
 Forum: Puzzles 2020-04-12, 22:10 Replies: 44 Views: 5,762 Posted By 0scar I didn't look at your Excel file before. ... I didn't look at your Excel file before. According to your computations, after ten days the cities are contaminated ABOVE 100%. You noticed it, and you hid it with well placed if statements. But...
 Forum: Puzzles 2020-04-12, 17:09 Replies: 44 Views: 5,762 Posted By 0scar A simple counterexample. There is a small (but... A simple counterexample. There is a small (but strictly positive) chance that the infection never leaves town A in ten days. Or in ten months. Or in ten thousand years.
 Forum: Puzzles 2020-04-10, 08:06 Replies: 44 Views: 5,762 Posted By 0scar If so, I apologise. Of course, the text of... If so, I apologise. Of course, the text of April 2020 problem is ambiguous. My first goal was to confirm that uau's interpretation of the problem is coherent with the given example. I restated...
 Forum: Puzzles 2020-04-08, 03:55 Replies: 44 Views: 5,762 Posted By 0scar Using the same strategy outlined by uau, I... Using the same strategy outlined by uau, I computed the sequence p(1) - p(10) for the given example: p(1) = 0 (E has distance 2 from A) p(2) ~= 0.00101080000 p(3) ~= 0.00651474676 p(4) ~=...
 Forum: Puzzles 2020-01-16, 03:34 Replies: 59 Views: 9,450 Posted By 0scar Using Newton's method, I found these... Using Newton's method, I found these coefficients: c0 = 1.316653736569374 c1 = -0.5038314121686646 c2 = 2.809476206784873 c3 = 4.927057764206701E-003 d0 = 0.3287562928937044 d1 =...
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