For a large-enough number of n participants, the average longest increasing subsequence is roughly proportional to the square root of n.

🤦 I can't subtract!

299 - 119 is 180, the same as you got.

Extra credit: How many different parallelograms in the field of stars on the US flag?

I found 324 different shapes of parallelogram. The smallest appeared at 124 different locations and orientations.

I was pleased to see there were more than zero but few enough to be listed.

I think I have a greedier cut for the second borehole. It removes 22% of the original sphere. That's going to affect which are the greediest boreholes after that.

Here are my first three cuts.

After some code optimization and more than 8 hours of computer time, I was able to calculate the 7th bipyramid. It took 463 times as long as the time to calculate the 6th bipyramid.

Regular: How many distinct paths are there from the top of the rhombus to the bottom if (1) you never visit the same point twice and (2) you move only downward or sideways?

Let's count them up ...

This is the answer I got.

Somehow I was expecting something simpler.

Extra credit: Within the interval (a, b), how likely is it that p4 > p7?

Let c = value of p where p7 = p4.

Then the answer is (b - c) / (b - a).

But what if 2 trees are equally far away, such as (7,4) and (8,1)?

Now the relative size of the gaps depends on the exact visibility. (The tree at (8,1)'s gap is larger 60% of the time.) It doesn't settle one way or the other no matter how large your visibility gets.

As your visibility grows, the gaps get smaller but their size relative to each other stays the same.

#ThisWeeksFiddler 28 Mar 2025 EC

There seems to be a pattern for the number of teams that can never win a tournament. If the number of teams in the tournament is 2^k, then the number of teams that can never win is 2^(k-1) - k + 1 (in the general case).