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 Showing results 1 to 25 of 115 Search took 0.02 seconds. Search: Posts Made By: uau
 Forum: Puzzles 2021-09-17, 17:26 Replies: 14 Views: 2,045 Posted By uau By the way the 175 limit for the bonus question... By the way the 175 limit for the bonus question seems very lax. Can it actually be said to be harder than the main question? Is there any natural way to solve it which would fail to also get 175 for...
 Forum: Puzzles 2021-09-16, 21:23 Replies: 14 Views: 2,045 Posted By uau I got 40 for the base problem and 144 for bonus. I got 40 for the base problem and 144 for bonus.
 Forum: Puzzles 2021-09-06, 11:24 Replies: 3 Views: 600 Posted By uau Yes, that is not always the correct strategy for... Yes, that is not always the correct strategy for the participants. If you haven't seen the triangular duel puzzle before, see that for analysis ("deliberately miss" may not be a directly valid option...
 Forum: Puzzles 2021-09-06, 01:37 Replies: 58 Views: 1,657 Posted By uau See post #32. You get an equation for half the... See post #32. You get an equation for half the lake sector angle like tan(x) * (\tau / 2 + 2*x) = 4, the solution to which probably isn't expressible with elementary functions so needs to be solved...
 Forum: Puzzles 2021-09-05, 20:06 Replies: 58 Views: 1,657 Posted By uau I'm not requiring the added surface to match the... I'm not requiring the added surface to match the boundary of the square, so for a small enough added surface area the solution would be a half sphere. However, on a unit square you could fit one with...
 Forum: Puzzles 2021-09-05, 18:31 Replies: 58 Views: 1,657 Posted By uau Anyone have ideas for how to solve a 3D version?... Anyone have ideas for how to solve a 3D version? For example, if you have a unit square and 2 units of freely shapeable surface, what's the maximum volume you can enclose?
 Forum: Puzzles 2021-09-01, 15:15 Replies: 58 Views: 1,657 Posted By uau I think it should follow from a half circle being... I think it should follow from a half circle being optimal in the straight-line case. By zooming close enough to any smooth curve, you can approximate it arbitrarily closely by a straight line. So...
 Forum: Puzzles 2021-08-31, 17:29 Replies: 58 Views: 1,657 Posted By uau What's your point? This was a question about a... What's your point? This was a question about a circular lake. Yes, the answer is smaller than in the straight line case (a half circle is the optimal answer there). So what?
 Forum: Puzzles 2021-08-31, 11:11 Replies: 58 Views: 1,657 Posted By uau If by "angle at the center of the lake" you mean... If by "angle at the center of the lake" you mean the angle of the lake sector between the fence endpoints, that was in my earlier post: it's 1.4362668, which is less than 90 degrees. There is a...
 Forum: Puzzles 2021-08-31, 00:52 Replies: 58 Views: 1,657 Posted By uau Seems to match the values I calculated... Seems to match the values I calculated (1.90317905 * 50^2 = 4757.947625).
 Forum: Puzzles 2021-08-30, 17:44 Replies: 58 Views: 1,657 Posted By uau For the circular lake case, I get for lake... For the circular lake case, I get for lake radius=1 and fence length=4: lake sector angle for fence endpoints = 1.4362668 distance between fence endpoints = 1.3159604 fence circle radius =...
 Forum: Puzzles 2021-08-30, 15:11 Replies: 58 Views: 1,657 Posted By uau Not necessarily a circle arc, but all parts will... Not necessarily a circle arc, but all parts will be circle arcs of equal curvature. Note that I've consistently used plural. In the extreme case where the path is just long enough, you could approach...
 Forum: Puzzles 2021-08-30, 14:25 Replies: 58 Views: 1,657 Posted By uau You always get circle segments, that's what my... You always get circle segments, that's what my proof showed. Compare this to a problem of finding the shortest path between two points that avoids obstacles. Any part of the path in free space must...
 Forum: Puzzles 2021-08-30, 13:31 Replies: 58 Views: 1,657 Posted By uau That is not a counterexample. The second image is... That is not a counterexample. The second image is wrong and does not have maximal area for that line length. An easy way to see that it must be wrong is that you could move the bases of the straight...
 Forum: Puzzles 2021-08-30, 11:03 Replies: 58 Views: 1,657 Posted By uau In any problem like this, each part should at... In any problem like this, each part should at least locally be a circle segment. If you have two points and a freely shaped path of a certain length between them, unless that path is a circle...
 Forum: Puzzles 2021-08-28, 21:28 Replies: 2 Views: 233 Posted By uau If you multiply the elements of the set {b^i for... If you multiply the elements of the set {b^i for all i} by b, you get the same set with permuted elements. Thus multiplying the sum by b does not change it mod n. Thus S*b = S mod n, S*(b-1)=0 mod n,...
 Forum: Puzzles 2021-07-07, 13:16 Replies: 35 Views: 3,575 Posted By uau There's a solution link now - but currently it... There's a solution link now - but currently it doesn't seem to work... (shows some general page)
 Forum: Puzzles 2021-06-26, 21:46 Replies: 35 Views: 3,575 Posted By uau I didn't "prove" it prime - in fact I explicitly... I didn't "prove" it prime - in fact I explicitly turned proofs off in Sage to speed things up (I'm not sure why they're enabled by default, seems silly to me). The unrealistic chance that a...
 Forum: Puzzles 2021-06-25, 18:57 Replies: 35 Views: 3,575 Posted By uau With Sage, generating all solutions up to 10^1000... With Sage, generating all solutions up to 10^1000 was pretty fast (there are 25 including the example solutions). I tried generating one with more digits, and got a solution above 10^9000.
 Forum: Puzzles 2021-06-05, 18:42 Replies: 20 Views: 3,163 Posted By uau It occurred to me that you can also get... It occurred to me that you can also get O(n*log(n)) by kind of the opposite strategy: instead of proving for one element at a time what its correct value must be, you can also collect permutations...
 Forum: Puzzles 2021-06-03, 00:03 Replies: 20 Views: 3,163 Posted By uau I'm pretty sure O(n*log(n)) is possible on... I'm pretty sure O(n*log(n)) is possible on average. For that it's enough that you can find a single correct position in O(log(n)) tries on average, and then repeat that for the remaining problem of...
 Forum: Puzzles 2021-06-02, 22:54 Replies: 20 Views: 3,163 Posted By uau By "bisection strategy", I meant something like... By "bisection strategy", I meant something like trying to rotate large blocks of guesses (if your permutation was 012345, rotating 3 first gets 120345). If the block was originally all correct, it's...
 Forum: Puzzles 2021-06-02, 21:32 Replies: 20 Views: 3,163 Posted By uau Trying something that could be the correct answer... Trying something that could be the correct answer given all previous ones (which I believe is what Walter's code does) is not always the optimal answer, either for average or worst-case behavior (at...
 Forum: Puzzles 2021-06-02, 21:14 Replies: 20 Views: 3,163 Posted By uau I'm not familiar with docplex which seems to be... I'm not familiar with docplex which seems to be what the code uses to generate the specific guesses, but it seems like it probably just chooses some arbitrary permutation which has the given number...
 Forum: Puzzles 2021-06-02, 00:50 Replies: 35 Views: 3,575 Posted By uau The second required property is completely... The second required property is completely meaningless as currently phrased. I assume it should say the numbers have to be at least 2.
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