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Search: Posts Made By: 0scar
Forum: Puzzles 2020-10-14, 09:04
Replies: 21
Views: 1,280
Posted By 0scar
In my opinion, May19 and Oct18 (different area...

In my opinion, May19 and Oct18 (different area triangles) were much harder than Oct20.
Perhaps now many frequent solvers actually submitted wrong solutions or no solutions at all due to the...
Forum: Puzzles 2020-10-12, 18:09
Replies: 21
Views: 1,280
Posted By 0scar
"I think I'm paranoid / And complicated..." ...

"I think I'm paranoid / And complicated..."
(Garbage, Version 2.0, 1998)

At least, now the text seems unambiguous enough to ponder this problem...
Forum: Puzzles 2020-10-12, 03:06
Replies: 33
Views: 2,796
Posted By 0scar
I followed uau's suggestion. Given a RPS(n)...

I followed uau's suggestion.

Given a RPS(n) game, we can always extend it to a RPS(n+2) game:
aaavw
aaavw
aaa10
ww001
vv100
where A is the adjacency matrix of the RPS(n) game, V is a column...
Forum: Puzzles 2020-10-11, 10:31
Replies: 33
Views: 2,796
Posted By 0scar
After a slight modification, uau's "algebric"...

After a slight modification, uau's "algebric" construction also explains the RPS(13) game with 39 automorphisms (which is optimal, according to the paper referenced within September's solution)....
Forum: Puzzles 2020-10-07, 05:28
Replies: 33
Views: 2,796
Posted By 0scar
A very elegant construction, thanks uau! ...

A very elegant construction, thanks uau!

Another nice construction works for composite n and solves n=9.
Given two games RPS(a) and RPS(b), build a game RPS(a*b).

Let z = x*b+y, with...
Forum: Puzzles 2020-10-06, 10:53
Replies: 33
Views: 2,796
Posted By 0scar
As a lucky guess, I searched for RPS(n) games...

As a lucky guess, I searched for RPS(n) games which admit at least one n-cycle as an automorphism.
So they admit at least n automorphisms (by repeatedly applying the cyclic shift).
Can we get n*q...
Forum: Puzzles 2020-10-06, 10:41
Replies: 21
Views: 1,280
Posted By 0scar
Unless it implies that the chaos operator can let...

Unless it implies that the chaos operator can let the program move to next instruction or force a jump to an instruction from the list, an even more "chaotic" (and undocumented) behaviour.
Forum: Puzzles 2020-09-12, 03:25
Replies: 33
Views: 2,796
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: 1,758
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: 1,758
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: 1,758
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: 1,808
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: 6,356
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: 6,356
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: 6,356
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: 6,356
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: 6,356
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: 6,356
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: 10,065
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 =...
Showing results 1 to 19 of 19

 
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