Archive for the 'Puzzles' Category

How I Spent My Saturday — A Geeky Puzzle

I feel like I should record this, on the off-chance that it will save someone else from spending 18 hours glued to a computer screen missing the obvious. It will be of very limited interest.

Actually, let’s make it a puzzle.

So I have a php script — let’s call it A.php — which contains an html form introduced by the line < form method=POST action=”B.php” > .

There are no other calls to scripts anywhere else in A.php, and none at all in B.php.

So I enter the following in my browser’s address bar (I tried this in multiple browsers, all with the same results):

FOO/A.php?QUERYSTRING

(where of course FOO is a web address). This causes some php code to execute. That code checks to see if the query string is nonempty (which it always is at this point), and if so, it displays the form, with a submit button. Here is what happens next:

a) Roughly half the time, I hit the submit button, which calls B.php, which also executes, at which point my address bar shows FOO/B.php . This seems entirely normal.

b) The other half of the time, I hit the submit button, which causes A.php to execute a SECOND TIME (instead of calling B.php). (It now thinks the query string is empty so the form is not re-displayed.) At this point my address bar shows FOO/A.php/B.php (despite the fact that B.php was never called, or at least never executed).

There is absolutely no apparent pattern to when I get a) and when I get b). I sit at my damned screen for hours on end (this started at 6AM and ended at midnight), repeating the same input, sometimes getting a) and sometimes getting b), according to what looks to me like a series of fair coin flips.

So, because I am making **absolutely no changes** to the code, this **must** mean something is going on at the server end, right? So I move all the code to a completely different server, and get exactly the same behavior.

This is not behavior that’s easy to google for. I wasted a little time trying.

Right around midnight, the truth dawned on me.

And now I wonder: Would a programmer with the right background have been able to guess what the problem was quicker than I did? Like, maybe at least 17 hours quicker? Let’s make it a challenge.

Click here to comment or read others’ comments.

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Using a Brainteaser to Discover a Theorem

A Guest Post

by

Bennett Haselton

Nearly 9 years ago, Steven posted this brainteaser:

Here I have a well shuffled deck of 52 cards, half of them red and half of them black. I plan to slowly turn the cards face up, one at a time. You can raise your hand at any point — either just before I turn over the first card, or the second, or the third, et cetera. When you raise your hand, you win a prize if the next card I turn over is red.

What’s your strategy?

Read no further if you want to try and solve this brainteaser on your own first!

Continue reading ‘Using a Brainteaser to Discover a Theorem’

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Where I’ve Been

A couple of weeks ago, I was in Las Vegas for the annual meeting of the Association for Private Enterprise Education, where I was honored to give an invited plenary address.

From there, I went directly to Atlanta, where I gave a short talk at the Gathering for Gardner, honoring the legacy of Martin Gardner. There were a lot of other really cool talks too.

I am sorry that the Las Vegas talk was not recorded and that the recording from the Atlanta talk won’t be available for a few months. Therefore I sat down in front of my webcam and repeated both talks, sticking as close to the original words as my memory would allow. Unfortunately there is no way to recreate the audience reaction or the question and answer periods.

Click below to view either or both of those re-creations.

The second talk is essentially a six-minute excerpt from the first. It surely benefited from the discussions here, here and here, and most especially from the comments of Bennett Haselton.

A few more words about escalators for those who care about this kind of thing:
Continue reading ‘Where I’ve Been’

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Thanksgiving Puzzle

Suppose there are two vaccines available. Suppose also that:

  • Both vaccines have been shown to be 90% effective in double-blind clinical trials.
  • Vaccine X has rather unpleasant side effects, which disappear after about 24 hours. Vaccine Y appears to have no short term side effects at all.
  • Both vaccines are identical in all other relevant ways you can think of — cost, probability of long-term side effects, possibility of collateral benefits, etc.

Which vaccine do you prefer to receive, X or Y?

I’ll give my answer in a few days, or chime in sooner if someone else gives my answer first.

Hat tip to the ever-thoughtful Romans Pancs, who emailed me the relevant analysis.

Edited to add: Well, that didn’t take long. Jim Ancona nailed it in comment #2 — and expressed it so clearly that I feel no need to explain it in any words other than his.

I also want to commend the first of the two answers in Dave’s comment #1, which brings up another factor that hadn’t occurred to me. Of course (in Dave’s scenario) you won’t be the only one thinking this way, so it’s not clear that in equilibrium you’ll prefer X, but it is clear that some people will prefer X for Dave’s reason. Once enough of them have chosen X, you can be indifferent between X and Y.

Click here to comment or read others’ comments.

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Aftermath

The victors in last week’s crossword challenge were:

First place, with a score of 276/276: A tie between Dan Williams and Richard Kennaway.

Second place, but heartbreakingly close, with a score of 274/276: Another tie, between Tim Goodwyn and the team of Dan Grayson & Carol Livingstone

Third place: Paul Epps

Fourth Place: Eric Dinsdale

Fifth Place: A tie between Paul Grayson and Biopolitical

Thanks to all of the above and all the rest who participated.

Some notes:

1) There are 276 white boxes in the puzzle. I scored one point per box. Other scoring systems are possible, such as one point per word.

2) I am open to the possibility that some of the answers marked wrong are just as good as the answers counted as right. I’ll try to give this some thought.

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Wednesday Puzzle

Feeling isolated? Perhaps a crossword puzzle will help.

Click on the image to do the crossword puzzle on line, or click here for a printable pdf.

If you do the puzzle on line, you can click the “submit” button to bring up a form where you can enter your name and submit your solution. I will find a suitable way to honor the best submissions.

Meanwhile, please do not post spoilers!!!.

Update: Thanks to biopolitical, who pointed out that there was a problem with the clue for 24A. That clue is fixed now.

Thanks also to my Mom, who informed me that the pdf wasn’t printing properly. That’s fixed now too.

Click here to comment or read others’ comments.

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Thursday Puzzle/Science Lesson

nickelEvery day, a man comes to my door with a United States nickel in his hand. He asks me whether I’d prefer to examine the heads side (which is always painted either black or white) or the tails side (which is always painted either red or green). I choose each day according to my whims.

And the same thing happens to my sister. Different man, different coin, but each day he’s there with a painted nickel, offering to let her examine either the heads side or the tails side.

Sometimes we call each other to compare notes on the colors we’ve seen. Here’s what we’ve concluded:

The Rules

  1. Our heads sides are never both white.
  2. Whenever one of our tail sides is green, the other one’s heads side is white.

We have thousands of observations to support these conclusions: On days when we both examine our heads sides, we never both see white. On days when we examine opposite sides and one sees a green tail, the other always sees a white head.

The Brain Teaser: Today we both chose Tails and both saw green. What colors were on our Heads sides?

Solution: By point 2) above, they were both white. But by point 1) above, that can’t happen. So….?

So what now?

Continue reading ‘Thursday Puzzle/Science Lesson’

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Escalators (The Geeky Version)

I hadn’t expected this escalator business (and see also here) to go on so long, but there have been a lot of smart comments, and a lot of smart disagreements, and a lot of smart changing and re-changing of minds, some of it the unavoidable consequence of the fact that we might all be using language a little differently.

So here is the geeky (i.e. precise!) version of what I want to say.

I. Your journey consists of some time on the stairs and some time on the escalator. You rest for a total of one minute, which you can take on the stairs or on the escalator (or split it if you like).

II. Define some constants:

W = your walking speed

V = the escalator speed

L = the distance from your starting point to your destination

Continue reading ‘Escalators (The Geeky Version)’

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Escalating Matters

There were a lot of great comments on my recent post about escalators, but none better than Bennett Haselton’s, which is so good I want to highlight here in a separate post.

I’m going to strip his argument down to make it even simpler, but this is all Bennett’s idea:

A New Puzzle: You’re boarding an escalator precisely at noon. You know that on a normal day, if you walk the entire way, the ride takes exactly ten minutes. But you also know that this is not a normal day, because the escalator is scheduled to be stopped for maintenance beginning at 12:05, and will at that point turn into the equivalent of a stairway. You’re planning to take a one-minute rest from walking at some point along your journey. Should you rest before 12:05, when the escalator is moving, or after 12:05, when the escalator is stopped?

Answer One:Of course you should rest while the escalator is moving, because that way, at least you make some progress while you rest.

Answer One, Reworded: Of course you shouldn’t rest while the escalator is stopped, because then you’ll spend an entire minute not getting anywhere.

Here’s the thing about Answer One: It’s completely wrong. It doesn’t make a bit of difference whether you rest from 12:00 to 12:01 or from 12:05 to 12:06 or for any other minute in between. If you don’t believe me, try an example: Suppose the escalator travels, oh, say, 20 yards per minute and your walking speed is 10 yards per minute. Then if you rest from 12:00 to 12:01, with the elevator moving, you’ll have traveled 160 yards by 12:07, and will continue to gain ten yards per minute after that. If instead you rest from 12:05 to 12:06 with the escalator stopped, you’ll have traveled exactly the same 160 yards by 12:07, and will continue to gain exactly the same ten yards per minute after that.

The Old Puzzle: You’re going to travel on a 100 yard staircase followed by a 100 yard escalator. You’re planning to take a one minute rest somewhere along the way. Should you take it on the stairs or on the escalator?

Answer One: You should rest on the escalator, because at least that way you make some progress while you rest. Or to put this another way, you shouldn’t rest on the stairs because then you’ll spend an entire minute not getting anywhere.

This time Answer One gives the right conclusion. But the reasoning can’t be right, because it’s the exact same reasoning that we applied to the New Puzzle, whereupon that reasoning led us totally astray.

Bennett’s lovely example illustrates as starkly as possible why we must reject Answer One even though it sometimes yields the right conclusion. The reason is that it also sometimes leads to the wrong conclusion. I’ve been trying to argue in the abstract that the logic of Answer One makes no sense; Bennett has done us the awesome service of pointing to a concrete example where that logic leads you inarguably astray.

It also illustrates my other main point: The real reason to rest on the escalator in the Old Puzzle is that resting on the escalator buys you more time on the escalator. Bennett has removed that advantage by giving you exactly five minutes on the escalator regardless of where you rest. In other words, when you cook up an example (like Bennett’s) in which resting on the escalator doesn’t buy you more time on the escalator, the argument for resting on the escalator vanishes in a puff of smoke.

This, incidentally, is related to a cryptic comment of my own on that earlier post, where I replied to an inquiry from Bob Murphy about my observation in an old Slate column that the fundamental confusion arises from measuring benefits in distance instead of time. (I claim that this is, in a sense that might not be entirely obvious, an equivalent description of the problem with Answer One.) In the Old Puzzle, you’re on the escalator for a fixed distance; in Bennett’s New Puzzle, you’re on the escalator for a fixed time. That illustrates exactly the distinction I had in mind, and if I find the time, I’ll write out the details sometime soon.

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Ups and Downs

escalator_photo_2

There are two kinds of people in this world: The first kind wonders why people stand still on escalators but not on stairs. The second kind wonders what’s wrong with the first kind. After all, if you stand still on the stairs you never get anywhere.

But people of the first kind are not usually dumb. I could give you a long list of top-rate economists and mathematicians who have been stumped by this puzzle. But I could also give you a long list of equally smart people who have been stumped by why anybody thinks it’s a puzzle in the first place. It’s come up again several times recently, because I included it in Can You Outsmart an Economist? and because I talked about it on my podcast with Bob Murphy, which generated a small flurry of email from listeners. So let me try once again to explain what’s going on here.

Let’s divide this into two parts: First, what’s the right way to think about this problem? Second, why is it a problem in the first place?

Continue reading ‘Ups and Downs’

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Megamillions

megamillions

Is it rational to play Megamillions, with the current jackpot of a billion dollars or so?

Yes and no. Here are three questions:

  1. Are you willing to pay $20 for ten MegaMillions tickets?
  2. Are you willing to pay $20 for seven weeks’ worth of immunity from fatal lightning strikes?
  3. I propose to flip a coin. Heads, you get the MegaMillions jackpot. Tails, you die. Do you want to play?

There is no irrational answer to any of these questions. Some people like to play the lottery; some don’t. Some people are safety fanatics; some aren’t. Some, but not all, love huge risks with huge potential payouts.

But there is such a thing as an irrational pattern of answers. I know there are millions who answer yes to question 1, because I see them buying tickets. I’m guessing that almost all of those people would answer no to question 2. And I’m guessing that a fair number of those would answer no to question 3 as well. Perhaps you”re one of that fair number. If so, I declare you irrational.

Ten Megamillions tickets give you about a one in thirty-million chance to win the jackpot. One in thirty-million is also pretty close to the chance you’ll be struck by lightning in the next seven weeks. If you’re willing to buy the lottery tickets but not immunity from the lightning, you’re telling me that winning the jackpot means more to you than staying alive. So you should go for the coin flip in question three. If you didn’t, I declare you irrational.

Well, so what? Some economist called you irrational. Why should you care?

You should care because this is exactly the kind of irrationality that will allow me to take all your money. Keep reading to see why.

But first, let’s acknowledge that I’ve ignored a few things, like the possibility that you’ll win one of the lesser prizes in the lottery. I’m assuming that, compared to the jackpot, those are negligible as reasons to buy a ticket. (This is consistent with the observed fact that a whole lot of people buy tickets only when the jackpot is large.) If you don’t like that assumption, we can avoid it by tweaking the numbers in the questions, in ways that I strongly suspect won’t change most people’s answers.

Now let’s get to the fun part where I take all your money. Suppose you’ve answered yes/no/no to the three questions above. Then I’ll rig up the following experiment: I fill a bag with 30 million white balls, one black ball, and one blue ball. I plan to pull a ball from the bag, but before I do, I’ll make you two offers. You can take them or leave them; it’s entirely up to you.

  • A. If you give me $20 upfront, and if I draw the blue ball, I’ll give you a billion dollars.
  • B. I’ll give you $20 upfront, provided you allow me to electrocute you if I draw the black ball.

You’ve already told me that you’d pay $20 for ten Megamillions tickets, giving you a one in thirty-million chance at roughly a billion dollars. So of course you’ll happily go for A. And you’ve already told you that it’s not worth it to you to give up $20 to avoid a one in thirty-million chance of electrocution. So of course you’ll also happily go for B.

So: You (voluntarily) give me $20 and accept my $20. So far we’re even. And, I might add, you’re very glad to be playing. You got two things and you wanted both of them.

Now the drawing. Most of the time I’ll draw a white ball, and nothing happens. But occasionally I’ll draw a blue or a black. When I do, I’ll tell you (perfectly honestly, because I’m honestly exploiting your irrationality, not trying to trick you) that I’ve drawn a non-white ball. There’s a fifty-fifty chance it’s black, in which case you will die, and a fifty-fifty chance it’s blue, in which case you win the billion. You are effectively facing the very coin flip that you told me in Question 3 that you prefer to avoid. Of course, then, you’ll gladly pay me a few bucks to call everything off. Now I’m ahead.

We might have to play this game several million times before I draw a non-white ball and take your money, but as long as you’re committed to your stated preferences, you should be willing to play several million times — or to let me set my computer to playing a virtual version for us several million times per hour. In a few hours, I’ll win some money from you. In another few hours, I’ll win more. And so on till you’re broke.

When an economist calls you irrational, it almost always means that if you follow through on your stated preferences, a sufficiently clever opponent can take all your money, leaving you smiling along the way. It’s worth being alert to such things.

If you thought this was fun, you should take the ten-question Irrationality Test in Chapter Six of Can You Outsmart an Economist?. Come back to the blog and let me know how you did.

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Monday Solution

The answer to Friday’s puzzle is YES. If I am a logic machine who only states what I can prove, and if I say “If I can prove there is no God, then there is no God”, it does follow that I can prove there is no God.

Once again, it was our commenter Leo who got this first (in Friday’s comment thread, graciously rot-13’d).

As with Thursday’s solution to Wednesday’s puzzle, there are two key relevant background facts:

A) An inconsistent system can prove anything.

B) A sufficiently complex consistent system cannot prove its own consistency. (This is Godel’s second incompleteness theorem.)

Here’s the logic:

1) I’ve asserted that “if I can prove there is no God, then there is no God”. We know that I assert only things that I can prove. Therefore I can prove this assertion.

2) That means I can also prove the equivalent assertion that “if there is a God, I cannot prove otherwise”.

3) Therefore, if I take my axioms and add the axiom “There is a God”, then I can prove that there is something I cannot prove.

4) Therefore, if I take my axioms and add the axiom “There is a God”, then I can prove that my axiom system is consistent (by Background Fact A.)

5) Therefore, if I take my axioms and add the axiom “There is a God”, my axiom system is inconsistent. (Because only an inconsistent system can prove its own consistency — that is, Background Fact B.)

6) Therefore the statement “There is a God” must contradict my axiom system.

7) This can happen only if my axiom system is able to prove that “There is no God”.

So yes, I can prove there is no God.

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Friday Puzzle

A followup to Wednesday’s puzzle:

The assumptions are the same as on Wednesday:

I am basically a logic machine. There are certain axioms that I believe, and I never say anything out loud unless it can be deduced from those axioms via the rules of logic. (Fortunately, I can talk about many things, because my axioms include everything from the usual axioms for arithmetic to a rich set of beliefs about ontology, ethics, psychology, and everything else I care about.)

Now I’ve found myself in a whole new imaginary conversation with the same old imaginary Bob Murphy. This time I found myself saying out loud that “If I can prove there is no God, then surely there is no God.”

The Puzzle: Can I in fact prove there is no God?

Solution forthcoming on Monday.

Click here to comment or read others’ comments.

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Thursday Solution

Here are the answers to yesterday’s puzzle. The first correct solution came from our commenter Leo (comment #18 on yesterday’s post).

The assumptions of the problem were: Everything I say out loud can be deduced from my axioms. My axioms include the ordinary axioms for arithmetic, among other things. And I recently said out loud that “I cannot prove that God does not exist”.

The questions were: Can I prove there is no God? Can I prove there is a God? And is there enough information her to determine whether there actually is a God?

The answers are yes, yes and no: Yes, I can prove there is no God. Yes, I can also prove there is a God. And no, you can’t use any of this to determine whether there is a God.

To explain, I’ll use the phrase “logical system” to refer to a system of axioms sufficiently strong to talk about basic arithmetic (and perhaps a whole lot of other things), together with the usual logical rules of inference. It’s given in the problem statement that I am a logical system.

Here are two background facts about logical systems:

A. An inconsistent logical system can prove anything at all. That’s because it’s tautological that if P is self-contradictory, then any statement of the form “P implies Q” is valid. If I’m inconsistent, that means I can prove at least one statement (call it P) that’s self-contradictory. Then if I want to prove, say, that the moon is made of green cheese, I note that:

  • I can prove P
  • It’s tautological that “P implies the moon is made of green cheese”
  • Therefore I can conclude by modus ponens that the moon is made of green cheese.

B. No consistent logical system can prove its own consistency. This is Godel’s celebrated Second Incompleteness Theorem.

Now here’s the argument:

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Wednesday Puzzle

Here’s what you should know about me: I am basically a logic machine. There are certain axioms that I believe, and I never say anything out loud unless it can be deduced from those axioms via the rules of logic. (Fortunately, I can talk about many things, because my axioms include everything from the usual axioms for arithmetic to a rich set of beliefs about ontology, ethics, psychology, and everything else I care about.)

Here’s what else you should know: Last night, in the course of an imaginary chat with an imaginary Bob Murphy, I found myself admitting out loud that “I cannot prove that there is no God.”

First Puzzle: Can I in fact prove that there is no God?

Second Puzzle: Can I prove that there is a God?

Third Puzzle: Based on the information given, can you determine whether there is a God?

I’ll answer tomorrow, or in a few days depending on how the comments play out.

Click here to comment or read others’ comments.

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Crossword Results

The results of the latest crossword contest:

Paul Epps and Alan Gunn submitted perfect solutions and therefore tied for first place.

Dan Christensen ran a close second with two incorrect letters, both in 15 across, and John Faben ran a close third with three incorrect letters, all in 35 across (which is too bad, because I’m rather fond of 35 across).

All four have earned signed books of their choice ( The Big Questions, The Armchair Economist, Fair Play, or More Sex is Safer Sex) — if you’re a winner, email me your selection and mailing address.

I’m electing not to post the solution in deference to others who might come along and prefer no-spoilers. But if there’s debate about a particular entry or two, I’m happy to engage.

Click here to comment or read others’ comments.

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Monday Puzzle

Have at it:

Click on the image to solve the puzzle. You’ll see a “save” button in the upper left in case you want to save your work and return to it later, and a “Submit” button if you want to submit your solution for judging. The three closest-to-perfect solutions will be acknowledged in this space and will receive appropriate rewards after the passage of a decent time interval (the length of which will be determined partly by the speed at which solutions arrive, but ought to be about a week).

Please try to keep spoilers out of the comments.

The rules are basically London Times rules:

  1. In most cases, there are two clues next to each other, one a straightforward definition and the other involving some wordplay. Part of your job is to figure out where one clue ends and the other begins. Example: “You could worship this mad dog” is a clue for GOD — “You could worship this” being the straight definition and “mad dog” being the wordplay. (Either could come first).
  2. Unlike in many American cryptics, there is sometimes a small connecting word that is not properly part of either clue.
  3. Internal punctuation means nothing. A question mark at the end of a clue is usually an acknowledgement that the clue is pretty lame. An exclamation point at the end usually means that the two clues overlap each other.
  4. Unlike in many American cryptics, not all clues are required to follow the above rules. There might be a few that deviate substantially, but in every case, once you know the solution, you ought to be able to say “Aha! I see how that’s a clue for that!”.

Click here to comment or read others’ comments.

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Boys, Girls and Hot Hands

This is a post about hot hands in basketball. But first, some relevant history:

The single most controversial topic ever broached here on The Big Questions was not Obamacare, or tax policy, or the advantages of genocide, or the policy treatment of psychic harms. It was this:

The answer, of course, is that you can’t know for sure, because (for example) by some extraordinary coincidence, the last 100,000 families in a row might have gotten boys on the first try. But in expectation, what fraction of the population is female? In other words, if there were many such countries, what fraction would you expect to observe on average?

The “official” answer — the answer, for example, that Google was apparently looking for when they posed this as an interview question — is that no stopping rule can change the fact that each birth has a 50% chance of being either male or female. Therefore the expected fraction of girls in the population is 50%.

That turns out to be wrong. It’s true that no stopping rule can change the fact that each birth has a 50% chance of being either male or female. From this it does follow that the expected number of girls is equal to the expected number of boys. But it does not follow that the expected fraction of girls in the population is 50%. Instead, that expected fraction depends on the country size, but is always less than 50%.

If you don’t see why, I encourage you to browse the archive of relevant blog posts. If you still don’t get it, I encourage you to keep browsing. Whatever your objections might be, you’ll find them addressed somewhere in the archive. I’m not interested in relitigating this. I will, however, happily renew my offer to take $5000 bets on the matter, on the terms described here. Last time around, all takers changed their minds before putting any money on the table.

Now let’s get to the hot hands.

Continue reading ‘Boys, Girls and Hot Hands’

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Are You Smarter Than Google? — Part Three

To review the bidding:

Two days ago I posed a puzzle about 10 pirates dividing 100 coins.

Yesterday, I presented what appears to be an airtight argument that the coins must be divided 96-0-1-0-1-0-1-0-1-0.

But yesterday I also told you that the “airtight argument” is in fact not airtight, and that other outcomes are possible. I challenged you to find another possible outcome, and to pinpoint the gap in the “airtight argument”.

Our commenter Xan rose to the occasion. (Incidentally, his website looks pretty interesting.) Here’s his solution:

Continue reading ‘Are You Smarter Than Google? — Part Three’

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Are You Smarter Than Google? — Part Two

treasureToday I’ll offer the “official” solution to yesterday’s puzzle — that is, the solution that Google has apparently expected from its job candidates. This is also the solution I gave when I first saw the puzzle, and the solution I usually get from my best students, and the solution given yesterday by some astute commenters.

But this solution has a gaping hole in it. Can you find it?

Continue reading ‘Are You Smarter Than Google? — Part Two’

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Are You Smarter Than Google?

pirateI’m not sure where this problem originated. I heard it first from John Conley, and have often assigned it to my classes. Google has used it to weed out job candidates. The answer that Google expects is the same answer I gave John Conley, and the answer I usually get from my best students. That answer is wrong. (Long time readers might feel a sense of deja vu.)

Can you get it right?

Here’s the problem:

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The Big Winners

The winners of our crossword puzzle contest are:

—Todd Trimble (3 mistakes)

—Eric Kehr (4 mistakes, but he corrected them all by email almost immediately)

—Serge Elnitsky (5 mistakes)

—Paul Epps (5 mistakes)

(There were supposed to be three winners, but since there’s a tie for third place, we have four.)

For all those who struggled and want to see the answers, I’m temporarily posting the solution here, but might take it down after a little while in case others want to try the puzzle without being tempted to peek.

Each winner is entitled to a copy of one of my books, with a personal inscription acknowledging your brilliance. If you’re a winner, please send me your mailing address by email and book choice by email or by commenting below.

The choices are:

The Armchair Economist — the principles of economics, applied to everyday life. Available both in the original (1993) edition and in the updated (2012) version. The latter is (I hope) a little better and a lot more up-to-date, but available only in paperback. The Wall Street Journal review is
here. You can read the preface to the 2012 version here.

Fair Play. The argument of this book is that we tend to think most seriously about issues like fairness when we’re explaining them to our children — so we should listen to things we say to children, draw lessons from them, and take those lessons into the marketplace and the voting booth. The Washington Post review is here. You can read a sample chapter here.

More Sex is Safer Sex. A compendium of surprises from economic theory, including how you can do your part to fight STDs by having more sex, and why you should contribute to only one charity. The Financial Times review is here. You can read an excerpt here.

The Big Questions — tackling the problems of philosophy, beginning with “Why is there something rather than nothing?”, using ideas from economics, mathematics and physics. Some reviews are here.

Continue reading ‘The Big Winners’

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Puzzle Contest Update

As of now, I’ve received exactly one completely correct answer to this week’s crossword. (The submission actually contained four errors, but it was followed almost immediately by an email from the submitter with the requisite four corrections, so I’m giving full credit.) Congratulations to our frequent commenter EricK.

The contest, however, remains open. I’ll be sending free autographed books (your choice of The Big Questions, The Armchair Economist, Fair Play, or More Sex is Safer Sex) to EricK and the three runners-up, where the runners-up will be determined by some yet-to-be-determined combination of accuracy and timeliness. The contest will close on a date still to be determined, but I plan to keep it open for at least another week. Keep those submissions coming!

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Monday Puzzles

Click image to solve puzzle.

So it turns out that if you take a notion to create a crossword puzzle, put it on your blog, and include a “submit” button so that solvers can send you their answers, then — at least if your skill set is similar to mine — writing the code to make that “submit” button work will be about twice as difficult and three times as time-consuming (but perhaps also several times as educational) as actually creating the crossword puzzle. I certainly learned some hard lessons about the difference between POST and GET. But it’s done and (I think) it works.

To do the puzzle online click here. For a printable version, click here. If you do this on line and want to submit your answer, use the spiffy “Submit” button! (And do feel free to compliment the author of that button!). The clues are subject to pretty much the same rules that you’d find in, say, the London Times or the Guardian.

I will gather the submissions and eventually give proper public credit to the most accurate and fastest solvers. Feel free to submit partial solutions; it’s not impossible that nobody will solve the whole thing.

Let’s try to keep spoilers out of the comments, at least for a week or so.

I have one very geeky addendum to all this, leading to a second Monday puzzle — one that might be easy to solve for a reader or two, but most definitely not for me. Unless you’re a very particular brand of geek, you’ll probably want to stop reading right here. But:

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Thursday Solution

Several commenters correctly solved yesterday’s puzzle…..

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Wednesday Puzzle

(Source omitted to discourage Googling; acknowledgements will come next week).

You have a sealed lockbox about a cubic yard in volume, containing $100,000 in hundred dollar bills. Your balance scale tells you that the box (with the money inside) weighs 100 pounds. You give the box to your friend Al, who flies it to the moon, while you, along with your balance scale, follow in a separate vehicle. Upon arrival, you retrieve the sealed box, put it on the balance scale and verify that it still weighs 100 pounds. You then give the box to your friend Barb, who loads it into her all-terrain vehicle and drives it to your moonbase, with you following along, again in a separate vehicle. When you get to the moonbase, Barb returns your lockbox. You open it and it’s empty.

Who stole your money, Al or Barb?

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Thursday Solution

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Tuesday Puzzle

Here I have a well shuffled deck of 52 cards, half of them red and half of them black. I plan to slowly turn the cards face up, one at a time. You can raise your hand at any point — either just before I turn over the first card, or the second, or the third, et cetera. When you raise your hand, you win a prize if the next card I turn over is red.

What’s your strategy?

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Friday Followup

Tuesday’s puzzle was hard, though our commenter Bennett Haselton nailed it. In case Bennett has nothing else to work on this weekend, here’s a much harder version.

Once again, Alice, Betty and Carol each has a postive integer stamped on her forehead. They know that two of the numbers add up to the third. This dialogue ensues:

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Tuesday Puzzle

Here’s a puzzle I hadn’t seen before. I’m concealing the source to discourage Googling, but will give credit where it’s due in a couple of days.

Alice, Betty and Carol each has a positive integer stamped on her forehead. They know that one of their numbers is equal to the sum of the other two. They proceed alphabetically around the table, each one either announcing her own number (if she’s managed to figure it out) or announcing that she doesn’t know it.

The game proceeds as follows:

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