Problem 150

[deinst]

"elememts" is a typo

[GraemeMcRae]

Also,
Problem 148: "wich" is a typo
Problem 154: "calulate" is a typo
Problem 155: "elecric" is a typo
Problem 158: "characterstrings" is a typo

(I'll let you slide on the double L's in words like cancelled, and the ou in colour as well as the -ise in standardise because people in some very remote parts of the world regard these spellings as -- though it may be hard to believe -- correct!)

[rayfil]

people in some very remote parts of the world

The English language was certainly not invented in the U.S. but adapted in that remote part of the world by immigrants from England who may not have had the highest of education at that time. Correct spelling all depends on perspective, doesn't it?

Thanks for spotting and reporting those typos.

[GraemeMcRae]

Correct spelling all depends on perspective, doesn't it?

Indeed. I was kidding, as I think you know. In just about all of the world outside the United States, the U.K. spelling is used, so we're the remote people. I don't know whether education is a factor, but I've heard that when a country is colonized, the language stops developing for a time. It somehow loses whatever momentum it had. The result, 200 years later, is a language in the colony that is very similar to that of the mother country 200 years ago. So not only does our notion of "correct" language vary from place to place, but also from time to time.

[JamieCamardelle]

I wonder if degenerate triangles should be considered - should a single term of the sequence sk be considered a subtriangle sum?

Expand

### spoiler removed - ed_r ###

[jaap]

I wonder if degenerate triangles should be considered - should a single term of the sequence sk be considered a subtriangle sum?

I think so, that would be a triangle of size 1.

[ed_r]

Jamie, your hidden text was a bit too close to being a spoiler. So I removed it.

[elr]

does triangles that made of a single number allowed ?

[rayfil]

Would you consider a single point as a triangle

[TripleM]

I can certainly draw a triangle around one number in the array.

[mvaneerde]

It might be worth considering the following clarification: upside-down triangles are not considered valid.

[rayfil]

From the problem description

Sub-triangles can start at any element of the array and extend down as far as we like (taking-in the two elements directly below it from the next row

Isn't that clear enough? How could you ever make valid upside-down triangles with that definition?

[mdean]

Just to make it perfectly clear, although chances are it won't be an issue, do triangles of size 1 count?

[mpiotte]

Just to make it perfectly clear, although chances are it won't be an issue, do triangles of size 1 count?

Yes they count.

But consider this. What is the minimum value of a triangle of size 1? And what is the mean and standard deviation of a triangle of size k filled with independent random variables distributed according to the generator output? (Ignoring the fact that these are pseudo-random only.)

[Flood1993]

Could someone confirm the following values? (Generating the triangle the same way)

For 10 rows:
-1***491

For 50 rows:
-1005***9

For 500 rows:
-190***504

Thank you

[dawghaus4]

I agree with 10 rows, but not 50 and 500 rows.

Tom

[drassont]

@Flood1993: I also get the same result as you for 10 rows, but not for 50 rows.