Author Archives: Jim Stevenson

NSA Track and Field Puzzle

This is a puzzle from Futility Closet.

“A puzzle by Steven T., a systems engineer at the National Security Agency, from the NSA’s September 2016 Puzzle Periodical:

Three athletes (and only three athletes) participate in a series of track and field events. Points are awarded for 1st, 2nd, and 3rd place in each event (the same points for each event, i.e. 1st always gets “x” points, 2nd always gets “y” points, 3rd always gets “z” points), with x > y > z > 0, and all point values being integers.

The athletes are named Adam, Bob, and Charlie.

  • Adam finished first overall with 22 points.
  • Bob won the Javelin event and finished with 9 points overall.
  • Charlie also finished with 9 points overall.

Question: Who finished second in the 100-meter dash (and why)?”

I thought this puzzle impossible at first.  There didn’t seem to be enough information to solve it.  But a bit of trial-and-error opened a path.

Answer.

See NSA Track and Field Puzzle for solutions.

Sphere and Plane Puzzle

This is another puzzle from BL’s Weekly Math Games.

“a + b + c = 2, and

a2 + b2 + c2 = 12

where a, b, and c are real numbers.  What is the difference between the maximum and minimum possible values of c?”

The original problem statement mentioned a fourth real number d, but I considered it a typo, since it was not involved in the problem.

Answer.

See Sphere and Plane Puzzle for a solution.

Mystery Quadratic

Presh Talwalkar has an interesting new problem.

“Students and teachers found a recent test in New Zealand to be confusing and challenging for covering topics that were not taught in class.

For the equation below, find the value of k for which the equation has numerically equal but opposite signs (for example, 2 and –2):”

The problem didn’t mention how old the students were, but the solution to another problem on the test indicates they needed to know calculus.

Answer.

See Mystery Quadratic for a solution.

Air Travel

This is a nice problem from Five Hundred Mathematical Challenges.

“Problem 62. A plane flies from A to B and back again with a constant engine speed.  Turn-around time may be neglected.  Will the travel time be more with a wind of constant speed blowing in the direction from A to B than in still air?  (Does your intuition agree?)”

Answer

See Air Travel for a solution.

A Voice From the Past

… I know I feel differently in the morning, after seeing the pictures and reading the stories of lives arbitrarily snuffed out and people who had little reduced to people who have nothing at all. But tonight I’m going to bed in a vicious mood, with a stomach so full of contempt for this poisoned republic and its brain-dead citizens that I can taste it in my mouth, like bile.

And the only thing I can think to ask God—if she does exists—is why, just for once, can’t you smite the wicked instead of the innocent?

Posted by billmon at 01:09 AM

(Billmon’s full post can now be found on the Internet Wayback Machine at  https://web.archive.org/web/20051001001007/http://billmon.org/)

This 24 September 2005 post was made during the height (or depths) of the Iraq War during the Bush-Cheney regime.  Also recall the other Bush debacle, Hurricane Katrina, was just the month before, August 23–31, 2005.  We thought we were in the depths of depravity and had no inkling that we were only at the higher rings of hell.

Survival of Records

I have written about this a bit in my “Symbolic Algebra Timelines” post as part of the discussion of how Greek mathematics got transmitted to the present.

I had read an article by the renowned literary historian Gilbert Highet some sixty years ago which I never forgot.  It discussed in some detail the miracle of the survival of records from the past.  I tried to find a copy online, but in vain.  So I purchased a used 1962 copy of the now extinct Horizons that contained the article and proceeded to digitize it.  Since the subject of the article is about disappearing writings of the past and how some managed to survive through reproduction, I feel it somewhat apropos that I allow it to see the light of day again.  He is a marvelous writer and covers the subject with fascinating detail.

Even with all the losses Highet records, writings still survived because they were in some sort of hard copy form. By 1962 fragile documents such as newspapers were being moved to microfilm.  But microfilm was often replaced by magnetic tape, which was in turn replaced by a succession of digital media: floppy discs, CDs, DVDs, memory sticks, and so on. Finally, local media is being replaced by files in the “cloud”. All these media are subject to deterioration and loss, or the whims of the custodians. And of course, they all need machines and software to retrieve their information—technology which may no longer exist. Terabytes of moon data are lost on Ampex magnetic tapes for which there are no analog tape readers or even records of the data formats. Even now, some books are being published electronically and not in hard copy.  Some people have referred to this ephemeral situation as the “digital Dark Age” where everything can be lost—often in an instant.  So perhaps we are lucky that records from the past were not digital.

My copy of Highet’s article appears in two forms: a full, but very large, version with all the color figures, Survival of Records (58 MB), and a text-only smaller version, Survival of Records wo figs (700 KB).

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