Sudorku redorx

Another, somewhat drier, question that occurred to me: what is the total number of possible solution grids for a sudoku puzzle? I.e., how many ways are there to consruct a 9x9 grid that has "the sudoku property"?

Su dork u

So this nonsense is popular now. I really don't get it - one grid filled with numbers is about the same as another, to me. With crossword puzzles, at least, the clues can be crafted with varying degrees of cleverness - not to mention 26 > 9.

However, it irks me that there might be peabrains running around getting good at these goofy puzzles and then having a valid claim of mental superiority when I can barely solve the "medium" puzzles in the Wed./Thurs. WaPo. So I've been practicin' some. It's all kind of tedious, but the most tedious part is checking the answer when I'm done.

So here's the nut: In the absence of an answer key, what is the fastest way to check that a su-dork-u grid contains one and only one of each digit in each row, column, and 3x3 box? Put another way: Call each row, column or box an "element"; what is the minimum number of elements that need to be checked for having each digit exactly once in order to be sure that all 27 elements have that property?

Doctored Photo #7

Identify the source of this edited photo and win ten points.

Doctored Photo #6

Here's a chance for a benchwarmer to get on the scoreboard. Five points.

Doctored Photo #5

This one should be within reach of casual news junkies. Ten points to whoever can identify the source.

Find non-prime, win beer cozy

I flipped through Douglas Copeland's book JPod this afternoon and noticed this passage:

Evil Mark stood up in the middle of the afternoon and said "I'm about to hand out sheets listing the 8,363 prime numbers between 10,000 and 100,000. Embedded in this list is one non-prime. First person to find that non-prime number wins my Family Guy promotional sixteen-ounce beer cozy."
In less than five minutes I won.
FUN FACT: any even number can be made by adding together two primes.

The next several pages contained lots of large numbers. The reference to Goldbach's Conjecture might suggest that there is an even number somewhere in the list, but that would seem a comedown from the guy who once encoded a passage in binary.

Any ideas?

Doctored Photo #4

Fifteen points to whoever can identify the source for this retouched photo.

Doctored Photo #3

Here's the most obscure picture so far, worth 20 points.

Doctored Photo #2

This photo is more obscure, and worth ten points if you can locate the unedited original.

Doctored Photo #1

The famous photo below has been doctored to remove the subject of interest. To play, comment with a link to a search that produces the original image in the first page of results. This picture is rated five points, with extra bragging rights if your first attempt finds multiple correct hits on the first page.

Dorks and dragons

So there's this kingdom, and in the kingdom is a lake. In the lake, there's an island, and on the island is a mountain. On the mountain lives a dragon, who's been devouring all the virgins in your village.


Dismayed at this state of affairs, you beard the dragon in his lair. The dragon sneers down at you, and says "I admire your courage, little dude. Tell you what: I propose a contest of wits. On the side of the mountain, there are thirteen poisoned wells, labeled 1-13. All the poisons taste the same - just like regular water. If someone/something drinks a cup of poison from well X, they will die unless they drink another cup of poison from a well numbered greater than X (within a reasonable amount of time). For example, if I drink from well 4, I will die unless I have a cup of poison from well 5 or well 6 or well 7, etc.. So... here's what I propose. Both you and I are rational thinkers. Lets each get a cup of water (without each other seeing) and, then exchange cups. We then do whatever we think is necessary to survive, but we must drink the cup offered to us. How's that for a deal?"

Fortunately for you, you got a look at the layout of the wells on your way to the lair, and you know the dragon has an ace up his sleeve: the dragon can get his water from any of the wells; however, well 13 is impossible for you to reach, being at the very top of the mountain and surrounded by insurmountable cliffs.

Do you take the deal? If so, what is your strategy?

Pirate shootout

Incensed at the imbalanced distribution of doubloons, Darrrian and Edwarrrd challenge Arrrthur to a duel, winner take all. They will stand at the corners of a triangle on the beach and take turns shooting. Each turn will consist of a pirate shooting at anyone he chooses, and the last pirate standing takes the gold. They draw straws to determine shooting order. If Arrrthur always kills his target, Darrrian kills his target 80% of the time, and Edwarrrd kills his target 50% of the time, what strategy should each pirate adopt? Who has the best odds of winning?

Pirate puzzle wankery

Five pirates (Arrrthur, Barrry, Charrrles, Darrrian and Edwarrrd) have stolen 100 doubloons and have agreed on a scheme to decide how to divide them:

Arrrthur must propose a division of the booty, and all the pirates then vote on this proposal.

If it fails to get a strict majority, Arrrthur is executed, Barrry proposes a division, and so on.

Each pirate follows a strategy whose descending priorities are: 1) remaining alive 2) getting maximum gold 3) killing others.

What division does Arrrthur propose?

Wonderlic IQ test

From the Atlantic.

Robert Jones, a star linebacker from East Carolina University, went to a pay phone outside the 1992 NFL Scouting Combine—the pre-draft ritual where professional football teams take stock of the college talent—and called his mother.

“Ma,” he said, “I’m sorry. I’m sorry.”

A top scout, Dave-Te’ Thomas, overheard the call. “Robert,” he asked, “what the hell is going on?”

“That question really threw me,” Jones replied.

The New York Giants had asked him a tough one: If he were on a capsizing boat with his mother and daughter and could save only one, which would he choose?

Besides dashing forty yards, bench-pressing 225 pounds, and weaving between cones, would-be professional football players must submit to full psychological workups before teams are willing to take the multimillion-dollar gamble of drafting them....

With playbooks approaching phone-book heft, however, intelligence has become a key measure of NFL draftees. The standard measure is the Wonderlic Personnel Test, a general intelligence exam taken by 2.5 million people seeking all types of work each year. It was first used in the NFL more than thirty years ago, and it has since been adopted by every team....

The only NFL player to score a perfect 50 was punter and Harvard alumnus Pat McInally, in 1975. (Scores are not officially released, but the results leak every year.) Only about 1 in 30,000 takers gets a perfect score, according to a 1992 study done by the testing company. The average score for NFL draftees over the past twenty years is a 19, which puts them a peg higher than aspiring drivers, deliverymen, and claims clerks, but not quite at the level of quality-control checkers (19.19), food-department managers (19.14), or machinists (19.54). The smartest group, on average, is attorneys (29.67), followed by editors (28.84) and executives (28.70). The lowest scorers, all around 15, are janitors, material handlers, and, in dead last, packers. A 10 is literacy, according to Wonderlic President Charlie Wonderlic Jr., and any score of 12 or under means the prospect is likely to be “successful using simple tools under consistent supervision.” At this year’s combine it was reported that Texas quarterback Vince Young, one of the draft’s top prospects, scored a 6 on the test. His agent contested the report, but did confirm that Young retook the test and scored a 16.

The Atlantic has a sample test (pdf) and ESPN has a five-minute version.

Deal or no deal

Suppose I present you with two boxes. I tell you that each box has a positive amount of money, and that one amount is double the other. I allow you to choose a box.

After you open it and determine how much is inside, I offer to let you switch to the other box in exchange for 10% of the amount in the first box. E.g., if your box has $10, I offer to sell you the other box for $1.

Should you take the deal, or should you keep your original box?

Smullyan revisited

As a further tribute to the genius of Raymond Smullyan, I present a somewhat more intimidating puzzle from his oeuvre. The hardest part is wading through the setup, but it's worth making the investment:

Inspector Craig of Scotland Yard was called to Transylvania to solve some cases of vampirism. Arriving there, he found the country inhabited both by vampires and humans. Vampires always lie and humans always tell the truth.

However, half the inhabitants, both human and vampire, are insane and totally deluded in their beliefs: all true propositions they believe false, and all false propositions they believe true. The other half of the inhabitants are completely sane: all true statements they know to be true, and all false statements they know to be false.

Thus sane humans and insane vampires make only true statements; insane humans and sane vampires make only false statements.

Inspector Craig met two sisters, Lucy and Minna. He knew that one was a vampire and one was a human, but knew nothing about the sanity of either. Here is the investigation:

Craig (to Lucy): Tell me about yourselves.
Lucy: We are both insane.
Craig (to Minna): Is that true?
Minna: Of course not!

From this, Craig was able to prove which of the sisters was the vampire. Which one was it?

Kicking things off

We'll inaugurate this venture with a very simple one from the venerable Raymond Smullyan.

Crack it if you can:

A dealer bought an article for $7, sold it for $8, bought it back for $9, and sold it for $10. How much profit did he make?