# Calendar Boy

Gary Foshee presented this puzzle at the 2010 Gathering for Gardner:

I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?

The first thing you think is ‘What has Tuesday got to do with it?’ Well, it has everything to do with it.

He proposed the answer 13/27, with this reasoning:

There are 14 equally likely possibilities for a single birth — (boy, Tuesday), (girl, Sunday), and so on.

If all we knew were that Foshee had two children, then it would seem that there are 142 = 196 equally likely possibilities as to their births.

But we know that at least one of his children is a (boy, Tuesday), and only 27 of the 196 outcomes meet this criterion. (There are 14 cases in which the (boy, Tuesday) is the firstborn child and 14 in which he’s born second, and we must remove the single case in which he’s counted twice.)

Of those 27 possibilities, 13 include two boys — 7 with (boy, Tuesday) as the first child and 7 with (boy, Tuesday) as the second child, and we subtract the one in which he’s counted twice. That, Foshee says, gives the answer 13/27.

This generated a lot of discussion when it appeared — unfortunately because the meaning of Foshee’s question is open to interpretation. See the end of this New Scientist article and the comments on Columbia statistician Andrew Gelman’s blog.

# Three in One

Dark Matter (2014), by the artistic collaborative Troika, manages to be a circle, a hexagon, and a square all at once.

The same group had created Squaring the Circle a year earlier.

# Quickie

If I roll three dice and multiply the three resulting numbers together, what is the probability that the product will be odd?

# Still Life

American furniture artist Wendell Castle’s 1978 Chair With Sports Coat is really neither — it’s an eye-deceiving sculpture carved from maple.

# “The Thirty-Six Dramatic Situations”

In 1895 French writer Georges Polti drew up a list of every dramatic situation that might arise in a story or performance, based on an earlier list drawn up by Venetian playwright Carlo Gozzi. They number only 36 — Polti listed the elements necessary for each:

1. Supplication (“a Persecutor, a Suppliant and a Power in authority, whose decision is doubtful”)
2. Deliverance (“an Unfortunate, a Threatener, a Rescuer”)
3. Crime Pursued by Vengeance (“an Avenger and a Criminal”)
4. Vengeance Taken for Kindred Upon Kindred (“Avenging Kinsman, Guilty Kinsman, Remembrance of the Victim, a Relative of Both”)
5. Pursuit (“Punishment and Fugitive”)
6. Disaster (“a Vanquished Power, a Victorious Enemy or a Messenger”)
7. Falling Prey to Cruelty or Misfortune (“an Unfortunate, a Master or a Misfortune”)
8. Revolt (“Tyrant and Conspirator”)
9. Daring Enterprise (“A Bold Leader, an Object, an Adversary”)
10. Abduction (“The Abductor, the Abducted; the Guardian”)
11. The Enigma (“Interrogator, Seeker and Problem”)
12. Obtaining (“A Solicitor and an Adversary Who Is Refusing, or an Arbitrator and Opposing Parties”)
13. Enmity of Kinsmen (“a Malevolent Kinsman; a Hated or Reciprocally Hating Kinsman”)
14. Rivalry of Kinsmen (“The Preferred Kinsman; the Rejected Kinsman; the Object”)
15. Murderous Adultery (“Two Adulterers; a Betrayed Husband or Wife”)
17. Fatal Imprudence (“The Imprudent; the Victim or the Object Lost”)
18. Involuntary Crimes of Love (“The Lover; the Beloved; the Revealer”)
19. Slaying of a Kinsman Unrecognized (“The Slayer; the Unrecognized Victim”)
20. Self-Sacrifice for an Ideal (“The Hero; the Ideal; the ‘Creditor’ or the Person or Thing Sacrificed”)
21. Self-Sacrifice for Kindred (“The Hero; the Kinsman; the ‘Creditor’ or the Person or Thing Sacrificed”)
22. All Sacrificed for a Passion (“The Lover; the Object of the Fatal Passion; the Person or Thing Sacrificed”)
23. Necessity of Sacrificing Loved Ones (“The Hero; the Beloved Victim; the Necessity for the Sacrifice”)
24. Rivalry of Superior and Inferior (“The Superior Rival; the Inferior Rival; the Object”)
25. Adultery (“A Deceived Husband or Wife; Two Adulterers”)
26. Crimes of Love (“The Lover; the Beloved”)
27. Discovery of the Dishonor of a Loved One (“The Discoverer; the Guilty One”)
28. Obstacles to Love (“Two Lovers; an Obstacle”)
29. An Enemy Loved (“The Beloved Enemy; the Lover; the Hater”)
30. Ambition (“An Ambitious Person; a Thing Coveted; an Adversary”)
31. Conflict With a God (“A Mortal; an Immortal”)
32. Mistaken Jealousy (“The Jealous One; The Object of Whose Possession He Is Jealous; the Supposed Accomplice; the Cause or the Author of the Mistake”)
33. Erroneous Judgment (“The Mistaken One; the Victim of the Mistake; the Cause or Author of the Mistake; the Guilty Person”)
34. Remorse (“The Culprit; the Victim or the Sin; the Interrogator”)
35. Recovery of a Lost One (“The Seeker; the One Found”)
36. Loss of Loved Ones (“A Kinsman Slain; a Kinsman Spectator; an Executioner”)

Each situation has its variations; for example, The Count of Monte Cristo is a Revenge for a False Accusation, a variation on the Crime Pursued by Vengeance; and Great Expectations is a Life Sacrificed for the Happiness of a Relative or Loved One, a variation on Self-Sacrifice for Kindred.

The whole book is here.

# The Inquisitive Artist

This sculpture, by Canadian artist Joe Fafard, has been scrutinizing passersby on Dundas Street in Toronto.

The principle is somewhat the same as Binary Arts’ mistrustful dragon.

# Disappearing Act

A puzzle by Joseph Horton, from MIT Technology Review, January-February 1999:

If the sun takes two minutes to set, what angle does it subtend from Earth?

# Podcast Episode 329: The Cock Lane Ghost

In 1759, ghostly rappings started up in the house of a parish clerk in London. In the months that followed they would incite a scandal against one man, an accusation from beyond the grave. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Cock Lane ghost, an enduring portrait of superstition and justice.

We’ll also see what you can get hit with at a sporting event and puzzle over some portentous soccer fields.

See full show notes …

# In a Word

hortulan
adj. of or belonging to a garden

micacious

bumfuzzle
v. to astound or bewilder

asomatous
adj. having no material body

Artist Gary Drostle designed this trompe l’oeil mosaic for a public garden in Croydon in 1996.

He calls it “the ideal low maintenance fishpond.”

# The Pizza Theorem

If you’re sharing a pizza with another person, there’s no need to cut it into precisely equal slices. Make four cuts at equal angles through an arbitrary point and take alternate slices, and you’ll both get the same amount of pizza.

Larry Carter and Stan Wagon came up with this “proof without words”: Each piece in an odd-numbered sector corresponds to a congruent piece in an even-numbered sector, and vice versa.

Also: If a pizza has thickness a and radius z, then its volume is pi z z a.

(Larry Carter and Stan Wagon, “Proof Without Words: Fair Allocation of a Pizza,” Mathematics Magazine 67:4 [October 1994], 267-267.)