trivia questions without answers

[Layne Bracy]

Hopefully we will know the answers this year.

1)Is there a ranked peak in Colorado whose rank is higher than its height(in feet)?

My guess is no. The lowest known ranked summit is 4711' Two Buttes. I suspect Colorado only has about 4000 ranked peaks.

2)What is the highest number X for which there are at least X peaks in Colorado with prominence X(feet)?

For example, Colorado has way over 300 peaks with prominence 300 feet. It does not have 1000 peaks with prominence 1000.

My guess is 750.

[glodder]

Very interesting questions, Layne. Do you have a mathematics background? I too am interested in such statistics.

I think your guesses are probably about right.

Todd

[Layne Bracy]

I am not a mathematician, but I play one on the internet!

Actually, math was my favorite subject growing up, and I majored in electrical engineering. However, I never took a formal statistics course.

If you like stats, here's another one for you - John Kirk did the compilation.

Of the 2300+ ranked peaks above 10K, only 12 have an elevation equal to that of a 40-ft contour interval. (e.g. Hagues Pk, 13560)

[John Kirk]

Good guesses Layne - 760 is the range of prominence where rank matches, and there are 4327 ranked peaks (for now), the lowest being 4711.

[CharlesD]

Of the 2300+ ranked peaks above 10K, only 12 have an elevation equal to that of a 40-ft contour interval. (e.g. Hagues Pk, 13560)

This is surprising! The naive math (2300/40) suggests that there should be 57+-2 that hit a multiple-of-40 elevation. 12 is many sigma off.

[Layne Bracy]

Yes, my conclusion is that it is inconvenient for the mapmakers to have an elevation precisely at the contour interval. So, consciously or not, they usually made the elevation falsely low or high to avoid the problem.

Also, in the few cases where the peak was assigned such an elevation, they usually did not draw in the higher contour but sometimes did.