Disappearing Act

Some amoebae, to be sure, do die. Sometimes an amoeba cannot get sufficient food or oxygen or moisture to sustain its life, and that kills it. But some amoebae do not get an opportunity to die … let us consider a well-fed, healthy amoeba alone in a drop of well-oxygenated pond water. I shall call it ‘Alvin.’ Alvin, let us suppose, lives happily through Tuesday and then, precisely at the stroke of midnight, Alvin divides, producing two offspring whom I shall call ‘Amos’ and ‘Ambrose.’ On Wednesday, we find two amoebae — Amos and Ambrose — swimming happily about in our drop of pond water. But what has become of Alvin? One thing is quite clear: Alvin is not an inhabitant of our drop of pond water on Wednesday. … His life, therefore, must have come to an end. But it is equally clear that Alvin did not die.

— Jay F. Rosenberg, Thinking Clearly About Death, 1983

December 10, 2013December 9, 2013 | Death

Lost History

Each year on the last Saturday in April, the citizens of Ocean Shores, Washington, celebrate “Undiscovery Day” to commemorate the night in 1792 when British explorer George Vancouver sailed right past their harbor without discovering it.

At midnight they gather on the shore and shout “Hey George — over here!”

December 9, 2013December 8, 2013 | History

Query

How are the following numbers arranged?

0, 2, 3, 6, 7, 1, 9, 4, 5, 8

	Select Click for Answer
In reverse alphabetical order.

December 9, 2013December 13, 2013 | Puzzles

Unquote

“When lost in a forest go always down hill. When lost in a philosophy or doctrine go upward.” — Ambrose Bierce

December 9, 2013December 8, 2013 | Quotations

Addition and Subtraction

In Mathematical Applications of Political Science, University of Minnesota political scientist William Riker describes a worrisome voting paradox that unfolded in the U.S. House of Representatives in 1956. At issue was a bill calling for federal aid for school construction; an amendment was proposed that would have offered this aid only to states whose schools were integrated. The House was divided into three interest groups:

Republicans opposed federal aid in general but supported integration. They would have preferred no bill at all but favored the amended bill to the original.
Northern Democrats wanted the amended bill but would accept the original bill rather than have no bill at all.
Southern Democrats, whose schools were segregated, favored the original bill but would prefer to have no bill rather than accept the amendment.

education bill bloc preferences

Clearly the original bill would have passed, as the Democrats as a group preferred it to having no bill at all. But, following procedure, the House voted first on whether to accept the amendment, and here the Republicans and the northern Democrats combined to support it, since both preferred the amended bill to the original bill. The second vote addressed whether to accept the now-amended bill, and now the Republicans and the southern Democrats united to kill it, since both preferred no bill to the amended bill.

So the original bill was popular, and the proposed amendment was popular, but combining them led to the bill’s defeat. “As if it were not enough that the choice may depend on the voting order, this fact can be used to twist the outcome of the legislative process,” Riker writes. “It may be possible to create a voting paradox such that no action is taken by the legislature even though a proposed bill would have passed prior to the creation of the paradox. A legislator could introduce an amendment to create such a paradox, and if the voting order were just right, the amended proposal would then be defeated.”

December 8, 2013December 8, 2013 | Society

Back Again

ernest a. mills

In 1929 the schooner A. Ernest Mills sank after a collision off the coast of North Carolina.

Four days later it bobbed to the surface again. Its cargo of salt had dissolved.

December 8, 2013December 8, 2013 | Oddities

Testament

In July 1945, a former inhabitant of Poland’s Lódz ghetto, Avraham Benkel, returned to find his home in ruins. Lódz had been the last of 200 ghettos in German-occupied Poland, and as the war neared its conclusion tens of thousands of its inhabitants had been deported to death camps. When the Red Army reached it in January, only 877 survivors remained.

In the abandoned building next door to his own, Benkel found a book, François Coppée’s The Truly Rich, on whose endpages and margins an anonymous boy had kept a diary of his ordeal:

June 1, 1944: “I just finished my ‘loaf, which I had to have for eight days; today is the third. It may turn [out] to be lethal for me to behave in such a manner, but my will-power is so weakened and my ever increasing appetite so strong that I can’t help it. Is there no bread, dry unsavoury bread enough for me and my fellow-sufferers in this world?”

July 10, 1944: “I am exhausted, I have no more patience, my nerves are frayed. What I do have is an indescribable disgust toward the world and mankind, toward the masses and people, toward doctrines and dogmas. I do not believe, I do not believe in any change in the world, no! Anyone who can sink as low as the modern man has can be nothing more than an unsuccessful experiment of nature, which certainly regrets it!”

July 20, 1944: “I feel such a need to open my diary and to write in order to ease my bitter heart, about what hell we go through, how terribly we suffer. During the time when we had literally nothing to eat, we were willing to believe that the physical annihilation of men, women, and children of our nation had appeased the blond beast. But now it looks as if they have not had enough, and that they want to satisfy their thirst with the blood of the innocent.”

Almost nothing is known about the boy’s identity, age, background, schooling, or fate. Only the verb forms in his entries tell us that he was male. In all likelihood he was deported to Auschwitz as the Russians closed in.

“My God, why do you allow them to say that you are neutral?” he wrote in a final, undated entry. “Why will you not punish, with all your wrath, those who are destroying us? Are we the sinners and they the righteous? Is that the truth? Surely you are intelligent enough to understand that is it not so, that we are not the sinners and they are not the Messiah!”

(From Alexandra Zapruder, Salvaged Pages: Young Writers’ Diaries of the Holocaust, 2002.)

December 7, 2013December 6, 2013 | History

Dog’s Mead

dog's mead puzzle

This puzzle was devised by W.T. Williams. The goal is to discover the age of Father Dunk’s mother-in-law (2 down), but the clues contain so much cross-reference and the grid so many interlocking solutions that practically the whole puzzle must be completed to find it.

The year is 1939. There are 20 shillings in a pound; 4840 square yards in an acre; a quarter of an acre in a rood; and 1760 yards in a mile.

ACROSS

1. Area in square yards of Dog’s Mead
5. Age of Martha, Father Dunk’s aunt
6. Difference in yards between length and breadth of Dog’s Mead
7. Number of roods in Dog’s Mead times 8 down
8. The year the Dunks acquired Dog’s Mead
10. Father Dunk’s age
11. Year of Mary’s birth
14. Perimeter in yards of Dog’s Mead
15. Cube of Father Dunk’s walking speed in miles per hour
16. 15 across minus 9 down

DOWN

1. Value in shillings per rood of Dog’s Mead
2. Square of the age of father Dunk’s mother-in-law
3. Age of Mary, father Dunk’s other daughter
4. Value in pounds of Dog’s Mead
6. Age of Ted, father Dunk’s son, who will be twice the age of his sister Mary in 1945
7. Square of the breadth of Dog’s Mead
8. Time in minutes it takes Father Dunk to walk 4/3 times round Dog’s Mead
9. The number which, when multiplied by 10 across, gives 10 down
10. See 9 down
12. Addition of the digits of 10 down plus 1
13. Number of years Dog’s Mead has been in the Dunk family

Hint: Start with 15 across, and keep your wits about you — most of the clues require some sort of insight or intelligent narrowing of the possible solutions; there’s very little mechanical plugging of numbers. With enough careful, dogged reasoning, it’s possible to complete the entire grid, but it’s stupendously hard.

	Select Click for Answer
Chris Adams sent me the guided solution below. Throughout, L is the length, B the breadth, and all units are in yards/square yards unless otherwise noted. Both 8 and 11 Across are years before 1939; since both are four digits, both must begin with a 1. The only two-digit cubes are 27 and 64, so 15 Across must be one of these numbers, and hence Father Dunk’s walking speed in miles per hour is either three or four. Let S denote his speed in miles per hour; then 88S/3 is his speed in yards per minute. And thus the time it takes him to walk the perimeter is 2(L+B)/(88S/3) = 3(L+B)/(44S), and so 4/3 this time (8 down) is (L+B)/(11S), and this is between 10 and 19 inclusive. Now, the perimeter is less than 1000 (since 14 Across is a three-digit number), so L+B, which is one half the perimeter, is less than 500. So L+B is equal to 11 times S times some number between 10 and 19, and this is lower than 500. Regardless of the value of S, 16 to 19 give us a value greater than 500, so the time is between 10 and 15 minutes. Look at 9 Down, 10 Across, and 10 Down. Since 9 Down ends in a 1, and 9 Down times 10 Across equals 10 Down, this means that 10 Across and 10 Down end in the same number. This also means that 8 Down ends with the same number that 15 Across begins with. And 15 Across begins with either 2 or 6, while 8 Down ends with 0, 1, 2, 3, 4, or 5. Hence that number must be a 2, so it takes 12 minutes, and the speed is 3 mph, which yields 27 as a cube. We know the speed and the time it takes to go 4/3 of the way around the perimeter, so we can solve for the perimeter and get that the perimeter is 792 yards. Alternatively, one can get that from L+B = 11×3×12, and P=2(L+B). Now, 12 Down is the sum of the digits in 10 Down, plus 1. This must be 19, as any other two-digit number ending in 9 is greater than any possible sum of the digits. Hence 10 Down must be 792, 882, or 972, making 10 Across 72, 82, or 92, respectively. Only in the first case does 10 Across divide 10 Down, since 792 equals 72×11. Hence 10 Down is 792, 10 Across is 72, and 9 Down is 11. This also makes 16 Across 16. 10 Down is a square and ends in 76, so B ends in either a 4 or a 6. Also, since L-B is less than 100, and L+B equals 396, B must be between 150 and 190, so there are eight possibilities for B. Of these, only 174 and 176 end in 76. However, 174 ends in 276, meaning Mary was born in the 1200s, which is plainly false (her father is only 72). Hence 76, which ends in 976, is the correct answer. The breadth B is 176, so the length L is 220, and this makes the area (1 Across) 38720. It also makes the number of roods 32, so 7 Across is 384. Also, 6 Across is 44, and so 6 Down is 48, which is Ted’s age. In six years, he’ll be 54, which is twice Mary’s age then. So she’ll be 27 then, which makes her 21 (3 Down) now. It also means she was born in 1918 (11 Across). Putting 8 Across and 13 Down together, we can fill in the blanks and show that the family acquired the property in 1110, so they’ve owned it for 829 years. 2 Down is a square number ending in 1, so the original number ends in 1 or 9. It is also in the 7000s, and since 80 squared is 6400 and 90 squared is 8100, this makes Father Dunk’s mother-in-law 81 or 89. 81 doesn’t work, but 89 squared is 7921, and so the mother-in-law is 89. 1 Down and 4 Down are still open, but we know that 1 Down is 5/8 (or 20/32, since there are 32 roods) of 4 Down. And 1 Down is between 300 and 400, so 4 Down must be between 480 and 640. Since 4 Down ends in 44, the only choice is 544, which makes 1 Down 340. This puzzle inspired an even harder one by CUNY math professor William Sit.

Click for Answer

dog's mead solution

Chris Adams sent me the guided solution below. Throughout, L is the length, B the breadth, and all units are in yards/square yards unless otherwise noted.

Both 8 and 11 Across are years before 1939; since both are four digits, both must begin with a 1.
The only two-digit cubes are 27 and 64, so 15 Across must be one of these numbers, and hence Father Dunk’s walking speed in miles per hour is either three or four. Let S denote his speed in miles per hour; then 88S/3 is his speed in yards per minute. And thus the time it takes him to walk the perimeter is 2(L+B)/(88S/3) = 3(L+B)/(44S), and so 4/3 this time (8 down) is (L+B)/(11S), and this is between 10 and 19 inclusive.
Now, the perimeter is less than 1000 (since 14 Across is a three-digit number), so L+B, which is one half the perimeter, is less than 500. So L+B is equal to 11 times S times some number between 10 and 19, and this is lower than 500. Regardless of the value of S, 16 to 19 give us a value greater than 500, so the time is between 10 and 15 minutes.
Look at 9 Down, 10 Across, and 10 Down. Since 9 Down ends in a 1, and 9 Down times 10 Across equals 10 Down, this means that 10 Across and 10 Down end in the same number. This also means that 8 Down ends with the same number that 15 Across begins with. And 15 Across begins with either 2 or 6, while 8 Down ends with 0, 1, 2, 3, 4, or 5. Hence that number must be a 2, so it takes 12 minutes, and the speed is 3 mph, which yields 27 as a cube.
We know the speed and the time it takes to go 4/3 of the way around the perimeter, so we can solve for the perimeter and get that the perimeter is 792 yards. Alternatively, one can get that from L+B = 11×3×12, and P=2(L+B).
Now, 12 Down is the sum of the digits in 10 Down, plus 1. This must be 19, as any other two-digit number ending in 9 is greater than any possible sum of the digits. Hence 10 Down must be 792, 882, or 972, making 10 Across 72, 82, or 92, respectively. Only in the first case does 10 Across divide 10 Down, since 792 equals 72×11. Hence 10 Down is 792, 10 Across is 72, and 9 Down is 11. This also makes 16 Across 16.
10 Down is a square and ends in 76, so B ends in either a 4 or a 6. Also, since L-B is less than 100, and L+B equals 396, B must be between 150 and 190, so there are eight possibilities for B. Of these, only 174 and 176 end in 76. However, 174 ends in 276, meaning Mary was born in the 1200s, which is plainly false (her father is only 72). Hence 76, which ends in 976, is the correct answer.
The breadth B is 176, so the length L is 220, and this makes the area (1 Across) 38720. It also makes the number of roods 32, so 7 Across is 384. Also, 6 Across is 44, and so 6 Down is 48, which is Ted’s age. In six years, he’ll be 54, which is twice Mary’s age then. So she’ll be 27 then, which makes her 21 (3 Down) now. It also means she was born in 1918 (11 Across).
Putting 8 Across and 13 Down together, we can fill in the blanks and show that the family acquired the property in 1110, so they’ve owned it for 829 years.
2 Down is a square number ending in 1, so the original number ends in 1 or 9. It is also in the 7000s, and since 80 squared is 6400 and 90 squared is 8100, this makes Father Dunk’s mother-in-law 81 or 89. 81 doesn’t work, but 89 squared is 7921, and so the mother-in-law is 89.
1 Down and 4 Down are still open, but we know that 1 Down is 5/8 (or 20/32, since there are 32 roods) of 4 Down. And 1 Down is between 300 and 400, so 4 Down must be between 480 and 640. Since 4 Down ends in 44, the only choice is 544, which makes 1 Down 340.

This puzzle inspired an even harder one by CUNY math professor William Sit.

December 7, 2013December 13, 2013 | Puzzles

Nicknames

Incontrovertibly the greatest nickname in history is The Snodgering Blee, Charles Dickens’ name for his eldest son, Charley. Some further inventive handles:

Thorpedo – Australian swimmer Ian Thorpe
Bathing Towel – Robert Baden-Powell
“Chariots” – English former rugby league and rugby union footballer Martin Offiah
“Singing” – Spanish cyclist Miguel Indurain
Attila the Hen – Margaret Thatcher
The Prince of Whales – George, Prince of Wales, later George IV (Leigh Hunt was sent to prison for calling him “a corpulent man of fifty”)
The Lizard of Oz – former Australian prime minister Paul Keating, after putting his arm around the queen in 1992
The Ambling Alp – Italian boxer Primo Carnera (6’5″, 260 lbs.)
Starvation Dundas – British Tory politician Henry Dundas, who said in a 1775 debate that he was “afraid” that a bruited famine in the American colonies “would not be produced” by a trade-restricting bill

The Doubleday publishing company was founded in 1897 by Frank Nelson Doubleday, whose initials inevitably led Rudyard Kipling to dub him “effendi.” In Ogden Nash, Douglas M. Parker says this was “a nickname he would carry for his entire career.”

December 6, 2013December 29, 2013 | Language

Shell Sense

In All Quiet on the Western Front, Erich Maria Remarque describes a battlefield reflex that is “far quicker, much more sure, less fallible, than consciousness”:

A man is walking along without thought or heed;–suddenly he throws himself down on the ground and a storm of fragments flies harmlessly over him;–yet he cannot remember either to have heard the shell coming or to have thought of flinging himself down. But had he not abandoned himself to the impulse he would now be a heap of mangled flesh. It is this other, this second sight in us, that has thrown us to the ground and saved us, without our knowing how.

Apparently this was a real phenomenon, at least in World War I. Stephen Foot, a British officer who spent three years on the western front, writes in his 1934 memoir Three Lives:

It was about this time that I suddenly realised that I had become acclimatised to shell fire; not that I liked or had ceased to fear it, but that I was able to discriminate between a shell that was coming near and one that was far enough away not to worry about. Some officers recently arrived from England were responsible. They were in charge of one of the working parties, and while we were standing in a group, not far from Plug Street, we heard the whine of a German shell. I looked instinctively in the direction of the church to see the usual cloud of dust and stones, and at the same time I realised that the officers with me had ducked. I was certainly no braver than they were — quite the contrary; but my ear had somehow become attuned, so that as soon as the first sound was heard I knew approximately where the shell would burst.

Foot calls this sense “a great relief to one’s nervous system” and speculates that the worst cases of nervous breakdown occurred in men who didn’t have it. “One cannot explain it,” Remarque wrote. “If it were not so, there would not be one man alive from Flanders to the Vosges.”

December 6, 2013December 5, 2013 | History