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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 =...
Showing results 1 to 12 of 12

 
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