I grew up reading Games magazine, so I was delighted when Ken Jennings posted a good old “Pic Tac Toe” on his blog. But when he recently posted a plea for others to do likewise, I thought it would be a good time to bring Conundrum out of its summer hibernation.

In a “Pic Tac Toe” puzzle, there are nine pictures in a three-by-three grid, like Tic-Tac-Toe. In each row, column, and diagonal, there is a common theme that unites the three pictures. The challenge is to find the eight themes.

You can click on each image to see a larger version:

I don’t have a message board like Ken has, so just post whatever you come up with in the comments section.

Enjoy!

UPDATE: Correct themes provided by Annalisa (4) and DeLisa (2). Alternate theme suggested by DeLisa (1). See comments for all answers.

Well, I’m off on vacation, and so I’ll be away from the blog for a few days.

I’ve posted some extra “content” this morning, and of course, here’s another Shakespeare Teacher Special Feature!

The rules are almost identical to the last Shakespeare Teacher Special Feature. Here’s how it breaks down:

• I. Thursday Morning Riddle: Please find below four brand-new riddles. Each riddle is numbered. Once you’ve solved the riddles, replace each number in the Venn Diagram below with the answer to the riddle that has that number.
• II. Shakespeare Anagram: Once the numbers have been replaced by the riddle answers, the letters in each circle of the Venn Diagram can be anagrammed into the title of a Shakespeare play. However, this can only be done after the question mark in the center section is replaced by a magic word. What is the magic word? And what are the three play titles?
• III. Conundrum: This week’s challenge is to come up with 26 words, any words commonly used in English, each of which features a different letter ______. (Fill in the blank with the magic word from the center section of the Venn Diagram.)

Use the comments section below to register any and all answers, discussion, and comments. I won’t be around for the next couple of days to moderate this, so please work together. If someone posts an answer you think is right, go ahead and say so and offer some words of encouragement. Also, feel free to pass this along to anyone you think may be interested. Here is the direct link.

The Riddles:

1. In stone primitive natural dwellings we lurk;
We think GEICO’s campaign was designed by a jerk;
But we’ve picked up a sitcom - a programming quirk;
And stay plural we must for this puzzle to work.

Who are we? (7 letters)

2. I’m a bag where potatoes are kept by the pound;
When your boss decides he doesn’t want you around;
If you hit me at night, you’ll be soon sleeping sound;
And I’ll bring any quarterback straight to the ground.

Who am I? (4 letters)

3. I’m the first in the spectrum that split light creates;
In the ledger, my presence a loss indicates;
I’m far left in the East, but I’m right in the States;
And the Hanrahan prefix in stories by Yeats.

Who am I? (3 letters)

4. I’m the boyfriend to Barbie who’s dapper and neat;
I’m the junior in baseball who’s primed to compete;
I’m the Cuckoo’s Nest novelist, sort of a beat;
And the Jeopardy champ who accomplished a feat.

Who am I? (3 letters)

So the solutions to this feature are four riddle answers, one magic word, three play titles, and up to 26 Conundrum words.

Good luck!

UPDATE: Riddles 1-4, Circles A, B, C, and the magic word all solved by Annalisa. Conundrum answers provided by Annalisa (22) and, in my own special way, me (4). See comments for all answers.

Well, I’m off to the Shakespeare Teacher institute. I’m very excited about being a part of this, but it means that I may have to step away from the blog for a few days. I’ll post when I can, but I’ll probably be more interested in blogging about the institute than in keeping up with my regular features.

But what if I could once again leave behind just one post that combines my most popular regular features for the week? Why, we’d just have to call that Shakespeare Teacher Special Feature II: The Magic Word! Here’s how it breaks down:

• I. Thursday Morning Riddle: Please find below four brand-new riddles. Each riddle is numbered. Once you’ve solved the riddles, replace each number in the Venn Diagram below with the answer to the riddle that has that number.
• II. Shakespeare Anagram: Once the numbers have been replaced by the riddle answers, the letters in each circle of the Venn Diagram can be anagrammed into the title of a Shakespeare play. However, this can only be done after the question mark in the center section is replaced by a magic word. What is the magic word? And what are the three play titles?

(Actually, the letters that form the magic word can form several words, but only one of the combinations will make sense to fill in the blank below.)

• III. Conundrum: Last week’s challenge was to come up with 26 words, plurals commonly used in English, each of which had a different final letter. This week’s challenge is to come up with 26 words, any words commonly used in English, each of which has a different ______ letter. (Fill in the blank with the magic word from the center section of the Venn Diagram.)

Use the comments section below to register any and all answers, discussion, and comments. I won’t be around much the next couple of days to moderate this, so please work together. If someone posts an answer you think is right, go ahead and say so and offer some words of encouragement. Also, feel free to pass this along to anyone you think may be interested. Here is the direct link.

The Riddles:

1. I’m a town or a bar where they might serve a sling;
The condition of clothing you might need to wring;
I’m a nurse that gives milk to another’s offspring;
And I’m slippery roads as Bon Jovi might sing.

Who am I? (3 letters)

2. Elementary I, eighty-eight on the table;
In the dorm or the lab, I’m a student who’s able;
I’m the god of the sun in Egyptians’ old fable;
And you say me three times when you hope your team’s stable.

Who am I? (2 letters)

3. I am found in Gerardo’s distinct greatest hit;
In a fifty-first state we may someday admit;
I am laws for when businessmen aren’t legit;
And a player in Just Cause who’s violent a bit.

Who am I? (4 letters)

4. I’m a poet Romantic and Mary’s fond spouse;
I am Ratcliffe’s own dog in a film by the Mouse;
I’m where Arafat’s death watch caused many to grouse;
And I’m surname to Hotspur - Northumberland’s house.

Who am I? (5 letters)

So the solutions to this feature are four riddle answers, one magic word, three play titles, and up to 26 Conundrum words.

Good luck!

UPDATE: Riddles 1-4, Circles A, B, C, and the magic word all solved by Annalisa. Conundrum answers provided by Annalisa (15) and me (5). See comments for answers. 6 letters still open.

My last Thursday Morning Riddle rhymed four words that each ended with a different letter. It reminded me of an earlier Conundrum that asked you to come up with rhymes for “zoo” without duplicating ending letters.

So, according to this guy, you can find 26 plurals, each of which ends in a different letter of the alphabet. I don’t know if that’s true or not, but let’s see what we can come up with.

He says you don’t need to use words which are both the singular and plural, fish and sheep for example, but I won’t make that restriction. We should probably stick to English, or words commonly used in English. I’ll also put no restrictions on how many responses each reader may post.

So from that post we already have H (fish), P (sheep), N (oxen), and I don’t think we need to worry about S. So that leaves 22 letters.

I’ll kick it off by starting at the beginning with A: data, media, criteria, etc.

21 to go. Any thoughts?

UPDATE: Responses provided by Kenneth W. Davis (3), Pseudo-Pedantius (5), and DeLisa (3), and me (5). 5 letters remain.

Via the Shakespeare Geek, we find an “amazing anagram” (which I have to say I never bothered to check):

To be or not to be: that is the question, whether tis nobler in the mind to suffer the slings and arrows of outrageous fortune.

Becomes:

In one of the Bard’s best-thought-of tragedies, our insistent hero, Hamlet, queries on two fronts about how life turns rotten.

That anagram has inspired this week’s Conundrum!

What well-known Shakespearean phrases can be anagramed from the following?

1. Tall Worthless Adage
2. Icky Backwashes Uncrowned Lord
3. Haberdasher Elf Slots Low Motto
4. Embrace Incoherent Hoot
5. Many Mourned Scorn Snifter

By the way, ShakespeareTeacher.com anagrams out to Search Peacemaker Ethos. I think that’s appropriate.

UPDATE: Anagram 2 solved by Annalisa. See comments for all answers.

I often like to come up with games of chance. There have been times in my life when this has been profitable, but mostly I’m just interested in questions of statistics and probability.

I had considered the math behind putting together my own Deal or No Deal style game, but with greatly reduced suitcase amounts and with a cost to play. Determining a fair cost (one which I would agree to if I were the player or the banker) at first seems like a hopelessly difficult problem, but the math is actually quite simple. The player has the option of keeping the initial suitcase until the end, and the banker has the option of offering whatever small amount he wants. At any given time the chosen suitcase is worth the average of all unopened cases. The banker certainly isn’t going to offer more, and if the player accepts less it’s just because he’s hedging his bets. The cost to play should be the average of all of the cases, whatever they may be.

A couple of months ago, while discussing the Two Envelopes problem, we briefly discussed what’s known as the Monty Hall problem, after the host of Let’s Make A Deal. Thinking of that problem has inspired another gambling proposition which is this week’s Conundrum.

Let’s continue to call our two gamblers the banker and the player. The banker has three boxes and hides a $10 bill in one of the boxes and a $1 bill in each of the other two. The player pays a set amount to the banker and chooses one of the three boxes. The banker must then open one of the other two boxes and show the player a $1 bill. Then the player can decide whether to keep the contents of the box he chose or switch to the other unopened box.

What would be the fair amount for the player to pay the banker to play this game?

UPDATE: Question solved by David. See comments for the answer.

In a Venn Diagram puzzle, there are three overlapping circles, marked A, B, and C. Each circle has a different rule about who or what can go inside. The challenge is to guess the rule for each circle. You can find a more detailed explanation of Venn Diagram puzzles, along with an example, here.

Since The Tudors wasn’t on this week, I offer you this Tudor-related puzzle to hold you over until Sunday. Each of the eight people below was a member of the court of King Henry VIII.

Have you figured out one of the rules? Two? All three? Feel free to post whatever you’ve got in the comments below. Just tell us which circle you’re solving, and what the rule is.

Enjoy!

UPDATE: Circles A and B solved by Annalisa. See comments for all answers.

How do they calculate the digits of pi?

I mean, they’ve calculated the number out to billions of places. When they get a billion digits out, how do they know they’re right? Just think about how incredibly precise that is. A quark’s diameter can be described in 18 decimal places, so surely a billion places is far beyond the realm of any practical scientific purpose or authentic human experience.

From a purely mathematical standpoint, pi is defined as the ratio between a circle’s circumference and its diameter. But the only way we have of measuring such things mathematically is by using pi.

Wikipedia has this article on the subject, but I doubt you’ll be suprised when I tell you it is not helpful to me. We could ask Daniel Tammet but he’d probably just tell us what the algorithm tastes like.

Anyway, if all this math stuff is boring to you, check out this discussion thread putting a more philosophical spin on the digits of pi:

“Somewhere inside the digits of pi is a representation for all of us — the atomic coordinates of all our atoms, our genetic code, all our thoughts, all our memories. Given this fact, all of us are alive, and hopefully happy, in pi. Pi makes us live forever. We all lead virtual lives in pi. We are immortal.” - Cliff Pickover

This means that we exist in pi, as if in a Matrix. This means that romance is never dead. Somewhere you are running through fields of wheat, holding hands with someone you love, as the sun sets — all in the digits of pi. You are happy. You will live forever.

Silly, perhaps, but technically true. And somewhere in the digits of pi, there’s a version of the Shakespeare Teacher who understands how they calculate the digits of pi.

Most crossword puzzles are two-dimensional. They have across and down clues.

This puzzle is one-dimensional. It has forward and backward clues. And all of the answers have to do with Shakespeare.

There’s not much space here, but imagine a horizontal row of 39 squares.

There are no black squares. All answers should be run together one after another with no spaces.

Post whatever you come up with. Feel free to use the comments section of this post to collaborate. The final answer will be a string of 39 letters that can be read in both directions.

Enjoy!

Forward (Left to Right)

1 - 8: Hamlet’s home

9 - 12: Briefly betrothed to Edward IV

13 - 16: The smallest fairy?

17 - 20: “A Lover’s Complaint”

21 - 26: Speaker of “If music be the food of love, play on”

27 - 32: Does Macbeth see one before him?

33 - 39: Twelfth Night’s Antonio once wore one (2 words)

Backward (Right to Left)

39 - 38: Scotland setting in Macbeth-like film

37 - 32: He is as constant as the northern star

31 - 29: Lear’s Fool will give you two crowns for one of these

28 - 23: The love of Venus

22 - 18: He loved Rosaline first

17 - 14: Companion to Hal and Falstaff at the Boar’s Head

13 - 11: What a piece of work it is!

10 - 5: He knows a bank where the wild thyme blows

4 - 1: Tempest setting

UPDATE: See comments for a big hint by Duane.

When I first started this blog, one of my very first posts suggested that almost all of the current natives of Mongolia and China were probably descendants of Genghis Khan. I literally had no readers at the time - I hadn’t yet told anyone about the blog - and so there was nobody to challenge my sweeping statement. I didn’t even make an argument. I’d like to give my argument now, and reopen the question as a Conundrum.

The idea was based on a National Geographic article about the biological legacy of Genghis Khan:

An international group of geneticists studying Y-chromosome data have found that nearly 8 percent of the men living in the region of the former Mongol empire carry y-chromosomes that are nearly identical. That translates to 0.5 percent of the male population in the world, or roughly 16 million descendants living today.

I went on to note:

16 million descendants. And that’s only men descended from Khan directly through the male line, father to son, for the past 800 years. The total number of Khan’s descendants living today is truly incalculable.

If you figure an average of four generations per century, that’s 32 generations between Genghis and his living descendants. Each person living today should have around 2 to the power of 32, or roughly 4.3 billion, living ancestors that are contemporary with Khan. Obviously, many individuals will have to be counted more than once, so let’s take a different tack.

Let’s pick a year somewhere between 1200 and 2000, say 1500. The total population of mainland Asia in 1500 was 268,400,000. Each living person today would have approximately 2 to the power of 20, or about a million, ancestors who were around in 1500 (and that’s if we don’t count anyone with a living parent).

So how many of the 268,400,000 around in 1500 were Khan’s descendants? Well, there are 16 million men living today that share the Y chomosome. If Khan and his direct male heirs had an average of 1.68 sons over 32 generations, that would give us our 16 million. That would only account for 505 men carrying that Y chromosome in 1500. But that calcuation leaves out two factors.

First, by 1500, Khan’s seed had been pretty well spread. The factors that account for his prevalence today came mostly into play during Khan’s life and the few generations following (see the article for details). So the distribution was a lot more top-heavy than the calculation above would suggest.

Second, we’re only counting direct male-line heirs. Passing a Y chromosome down from father to son over 32 generations is only one of 4.3 billion different permutations of inheritance. Each of those 16 million Y chromosome carriers alive today probably has an average of at least one sister or daughter. That doubles the known descendants right there. Extend that back over 32 generations, then consider all of their descendants, and you get the idea. If we change “average of 1.68 sons over 32 generations” (which we know is true) to “average of 2 children of either sex over 32 generations” (which doesn’t seem like too great of a leap from there), then 16 million becomes 4.3 billion, greater than the population of mainland Asia today.

It seems to me that today’s ethnic Mongolians and Chinese would almost all have to be descended from Khan, some many times over.

Now I am no math expert. I’m a Shakespeare Teacher. It’s very possible I could be wrong about this. I’d be interested to hear what other people think, particularly people with more professional experience with statistical analysis.

And I should also point out that I pin no political, moral, or judgmental significance to being a descendant of Genghis Khan. This is simply a math, history, and logistical Conundrum. I truly hope no offense is taken (though if you read my original post and the Economist article it is based on, it actually seems to be a point of pride for both Mongolia and China to be the descendants of Khan). And my family comes from Belarus, so this would mean I’m probably a descendant of Khan as well. So don’t screw with me.

Now, with all that in mind, for this week’s Conundrum, I hereby submit my original conclusion up for public scrutiny:

So, China and Mongolia should probably stop arguing over which of their people are the true heirs of Genghis Khan. My guess is, almost all of them are.