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Search: Posts Made By: uau
Forum: Puzzles 2021-10-09, 13:08
Replies: 37
Views: 1,105
Posted By uau
It's a constant shift cipher, not a general...

It's a constant shift cipher, not a general substitution cipher.
Forum: Puzzles 2021-10-05, 11:43
Replies: 20
Views: 3,003
Posted By uau
Well here is a slightly cleaned up version of the...

Well here is a slightly cleaned up version of the code I used. By default it uses a C routine to calculate optimal damage for given teams. You can disable that, and the pure Python code is still...
Forum: Puzzles 2021-10-04, 12:57
Replies: 20
Views: 3,003
Posted By uau
The teams in the example solution are ["4809",...

The teams in the example solution are ["4809", "5284", "1065", "1382", "3469"]. But the given match strings are not optimal for those teams. I get 160 damage for them. Looking at the given matches,...
Forum: Puzzles 2021-10-04, 12:50
Replies: 3
Views: 314
Posted By uau
The description of possible slide moves seems...

The description of possible slide moves seems lacking. It just says "can slide the rows and columns", which seems to imply arbitrary direction/amount of slide. After example of rows, for columns it...
Forum: Puzzles 2021-10-04, 11:24
Replies: 20
Views: 3,003
Posted By uau
["0381", "0645", "0896", "0923", "5279"] gives...

["0381", "0645", "0896", "0923", "5279"] gives 144 damage for the bonus question.

I found this by writing an exact solver for the best possible damage value for given teams, and then starting from...
Forum: Puzzles 2021-09-17, 17:26
Replies: 20
Views: 3,003
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: 20
Views: 3,003
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: 713
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 2,160
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: 347
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: 4,013
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: 4,013
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: 4,013
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: 3,361
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...
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