The Substitute

Between July 2015 and October 2018, the National Security Agency offered a monthly puzzle written by a staff member. Here’s the puzzle for October 2015, created by applied research mathematician Ben E.:

Kurt, a math professor, has to leave for a conference. At the airport, he realizes he forgot to find a substitute for the class he was teaching today! Before shutting his computer off for the flight, he sends an email: “Can one of you cover my class today? I’ll bake a pie for whomever can do it.” He sends the email to Julia, Michael, and Mary Ellen, his three closest friends in the math department, and boards the plane.

As Kurt is well-known for his delicious pies, Julia, Michael, and Mary Ellen are each eager to substitute for him. Julia, as department chair, knows which class Kurt had to teach, but she doesn’t know the time or building. Michael plays racquetball with Kurt so he knows what time Kurt teaches, but not the class or building. Mary Ellen helped Kurt secure a special projector for his class, so she knows what building Kurt’s class is in, but not the actual class or the time.

Julia, Michael, and Mary Ellen get together to figure out which class it is, and they all agree that the first person to figure out which class it is gets to teach it (and get Kurt’s pie). Unfortunately the college’s servers are down, so Julia brings a master list of all math classes taught that day. After crossing off each of their own classes, they are left with the following possibilities:

  • Calc 1 at 9 in North Hall
  • Calc 2 at noon in West Hall
  • Calc 1 at 3 in West Hall
  • Calc 1 at 10 in East Hall
  • Calc 2 at 10 in North Hall
  • Calc 1 at 10 in South Hall
  • Calc 1 at 10 in North Hall
  • Calc 2 at 11 in East Hall
  • Calc 3 at noon in West Hall
  • Calc 2 at noon in South Hall

After looking the list over, Julia says, “Does anyone know which class it is?” Michael and Mary Ellen immediately respond, “Well, you don’t.” Julia asks, “Do you?” Michael and Mary Ellen both shake their heads. Julia then smiles and says, “I do now. I hope he bakes me a chocolate peanut butter pie.”

Which class does Kurt need a substitute for?

Click for Answer
| Puzzles

Quarters

https://commons.wikimedia.org/wiki/File:Typy_kultury_organizacyjnej,_Ateny_II_(ubt).svg

USC mathematician Solomon Golomb offered this puzzle in his column, “Golomb’s Gambits,” in Johns Hopkins Magazine. How can you dissect this figure into four congruent pieces?

Click for Answer
| Puzzles

Old Booty’s Ghost

https://books.google.com/books?id=fKByQxeCmREC

A striking tale from the 18th century: It’s said that around 1687 a group of English mariners on the Italian coast were surprised to see “two men run by us with amazing swiftness”:

Captain Barnaby says, ‘Lord bless me, the foremost man looks like next door neighbour, old Booty;’ but said he did not know the other behind. Booty was dressed in grey clothes, and the one behind him in black; we saw them run into the burning mountain in the midst of the flames! on which we heard a terrible noise, too horrible to be described.

When they returned to Gravesend, Captain Barnaby’s wife said, “My dear, I have got some news to tell you; old Booty is dead.” Barnaby swore an oath and said, “We all saw him run into Hell!”

As the story goes, when word of this allegation reached Booty’s widow, she sued Barnaby for a thousand pounds. The punchline is that Booty’s appearance on the volcano was shown to have occurred within two minutes of his death, and when his coat was exhibited in the courtroom, 12 sailors swore that its buttons matched those of the fleeing man.

The Judge then said, ‘Lord grant I may never see the sight that you have seen; one, two, or three may be mistaken, but twenty or thirty cannot.’ So the widow lost her cause.

According to folklorist Jeremy Harte, this story appeared in print at least 19 times between the 1770s and the 1830s. It seems to have started among the dockyards of the lower Thames, where in one early version Booty was an unscrupulous contractor who had supplied the navy with adulterated beer — and his damnation was “a matter of just retribution for the sin he had committed.”

(Jeremy Harte, “Into the Burning Mountain: Legend, Literature, and Law in Booty v. Barnaby,” Folklore 125:3 [December 2014], 322-338.)

| Oddities

After You

A problem from Canada’s 2003 Hypatia contest:

Xavier and Yolanda are playing a game. They begin with two piles of three coins each and take turns; on each turn a player removes one or more coins from any one pile. The winner is the player who takes the very last coin. Xavier always goes first, but Yolanda has a strategy that ensures that she will always win. What is it?

Click for Answer
| Puzzles

“Half-Hanged Smith”

John Smith escaped execution three times. Convicted of housebreaking in 1705, he was hanged at the Tyburn gallows for a quarter of an hour before the people called for a reprieve and he was cut down.

When he had perfectly recovered his senses he was asked what were his feelings at the time of execution; to which he repeatedly replied, in substance, as follows. When he was turned off, he for some time was sensible of very great pain, occasioned by the weight of his body, and felt his spirits in a strange commotion, violently pressing upwards. That having forced their way to his head, he as it were saw a great blaze, or glaring light, which seemed to go out at his eyes with a flash, and then he lost all sense of pain. That after he was cut down, and began to come to himself, the blood and spirits, forcing themselves into their former channels, put him, by a sort of pricking or shooting, to such intolerable pain that he could have wished those hanged who had cut him down.

He returned to housebreaking on his release in 1706, but his strange luck continued: On his second indictment some difficulties in the case induced a panel of judges to set him free, and on his third the prosecutor died before the day of the trial.

The streak ended in 1727, when he was convicted of stealing a padlock and sentenced to transportation. He pleaded for corporal punishment instead but was sent to Virginia that July.

| Crime

Misc

https://commons.wikimedia.org/wiki/File:Pete_Conrad_on_LM_ladder,_Apollo_12.jpg

  • Peter Davison, who played the fifth Doctor in Doctor Who, is the father-in-law of David Tennant, who played the 10th.
  • Sharks are older than trees.
  • ABHORS, ALMOST, BEGINS, BIOPSY, and CHINTZ are alphabetical.
  • \displaystyle \sqrt{7! + 1} = 71
  • “The punishment can be remitted; the crime is everlasting.” — Ovid

“Whoopee! Man, that may have been a small one for Neil, but that’s a long one for me!” — Pete Conrad, after becoming the third human to set foot on the moon

| Entertainment · History · Language · Quotations · Science & Math · Trivia

Edge Case

https://commons.wikimedia.org/wiki/File:Universum.jpg
Image: Wikimedia Commons

Suppose … for a moment, all existing space to be bounded, and that a man runs forward to the uttermost borders, and stands upon the last verge of things, and then hurls forward a winged javelin,– suppose you that the dart, when hurled by the vivid force, shall take its way to the point the darter aimed at, or that something will take its stand in the path of its flight, and arrest it? For one or other of these things must happen. There is a dilemma here that you never can escape from.

— Lucretius, De rerum natura

| Oddities

A Sad Mystery

https://commons.wikimedia.org/wiki/File:Dead_seal,_South_Fork,_Upper_Wright_Valley_2016_01.jpg
Image: Wikimedia Commons

In 1903 Robert Falcon Scott made an odd discovery in the Dry Valleys of Antarctica:

[W]e have seen no living thing, not even a moss or a lichen; all that we did find, far inland amongst the moraine heaps, was the skeleton of a Weddell seal, and how that came there is beyond guessing. It is certainly a valley of the dead; even the great glacier which once pushed through it has withered away.

It appears that periodically a crabeater, Weddell, or leopard seal finds its way inland from McMurdo Sound and the Ross Sea and perishes in the punishing environment of the dry valleys, an extreme desert. There the dry conditions mummify its corpse, preserving it in some cases for thousands of years.

Some mummies have been found as much as 41 miles inland and as high as 5,900 feet above sea level, reflecting a heroic effort to find the sea. Mercifully the phenomenon is relatively rare, with a seal becoming lost only once every 4 to 8 years.

| Science & Math