Round Numbers

A circle is divided into six sectors, into which are written (say, counterclockwise) these numbers:

1, 0, 1, 0, 0, 0

You can increase any two neighboring numbers by 1. By doing this repeatedly, is there a way to make all six numbers equal?

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| Puzzles

Grime Dice

This remarkable phenomenon was discovered by Cambridge mathematician James Grime. Number five six-sided dice as follows:

A: 2, 2, 2, 7, 7, 7
B: 1, 1, 6, 6, 6, 6
C: 0, 5, 5, 5, 5, 5
D: 4, 4, 4, 4, 4, 9
E: 3, 3, 3, 3, 8, 8

Now, on average:

A beats B beats C beats D beats E beats A

and

A beats C beats E beats B beats D beats A.

Interestingly, though, if each die is rolled twice rather than once, then the first of the two chains above remains unchanged except that D now beats C — and the second chain is reversed:

A beats D beats B beats E beats C beats A.

As a result, if each of two opponents chooses one of the five dice, a third opponent can always find a remaining die that beats them both (so long as he’s allowed to choose whether the dice will be rolled once or twice).

(Ward Heilman and Nicholas Pasciuto, “What Nontransitive Dice Exist Among Us?,” Math Horizons 24:4 [April 2017], 14-17.)

| Science & Math

Correspondence

Excerpts from letters received by the British pensions office, quoted in George Lyttelton’s Commonplace Book, 2002:

  • Mrs R. has no clothes, has not had any for many years. The clergy have been visiting her.
  • In reply to your letter, I have already cohabited with your officers, so far without any result.
  • You have changed my little boy to a little girl. Will this make any difference?
  • Please send money at once, as I have fallen in errors with my landlord.
  • I have no children, as my husband is a bus-driver and works all day and night.
  • In accordance with your instructions, I have given birth to twins in the enclosed envelope.
  • I have been in bed with the doctor for a week, and he does not seem to be doing me any good. If things don’t improve I shall have to get another doctor.
  • Milk is wanted for the baby, and the father is unable to supply it.
  • The teeth on top are all right, but the ones in my bottom are hurting terribly.
| Humor

In a Word

subagitate
v. to have sex with

verecund
adj. bashful; modest

reme
v. to cry or call out

cacoëpistic
adj. badly pronounced

[Sir Walter Raleigh] loved a wench well; and one time getting up one of the Mayds of Honour up against a tree in a Wood (’twas his first Lady) who seemed at first boarding to be something fearfull of her Honour, and modest, she cryed, sweet Sir Walter, what doe you me ask? Will you undoe me? Nay, sweet Sir Walter! Sweet Sir Walter! Sir Walter! At last, as the danger and the pleasure at the same time grew higher, she cryed in the extasey, Swisser Swatter Swisser Swatter. She proved with child, and I doubt not but this Hero tooke care of them both, as also that the Product was more than an ordinary mortal.

— John Aubrey, Brief Lives, 1697

| History · Language

Place Settings

In his 1954 book Language in Relation to a Unified Theory of the Structure of Human Behavior, Kenneth Pike presents a toy language in which meaning is determined by the relative order of the elements. If these expressions have the indicated meanings:

1. los            "It is smoke"
2. mif            "It is a ball"
3. kap            "They are eyes"
4. losmif         "The ball is smoking"
5. miflos         "The smoke is rolling"
6. mifmif         "The ball is rolling"
7. mifmiflos      "The smoke is rolling in round puffs"
8. mifmifkap      "He is rolling his eyes around" or
                  "The eyes are rolling around"
9. losmifkap      "His eyes roam darkly"
10. mifkaplos     "The smoke is trying to escape" or
                  "The smoke looks around"
11. kapmifmif     "I can see the ball rolling"
12. mifkapkap     "He is looking around"
13. losloskap     "His eyes are smoldering menacingly"

… what would be meant by kapmiflos and kapkapkap?

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| Language