I’m thinking of a two-digit number that is not a prime, the sum of two primes, or the product of two primes.

What number am I thinking of?

You have defeated Iachimo at his own game, and he’s not happy.

“I usually go first,” he says icily. “Surely you will allow me a rematch, and allow me to go first this time.”

You know that, with his standard set up using piles of 1, 2, 3, 4, and 5, he can force a win by going first, so you decline. But he comes up with a surprising offer: you can increase the number of piles.

As before, the piles will start at 1 coin and will increase by 1 coin until the desired number of piles is reached. So if you decide to increase to six piles, the coin amounts must be 1, 2, 3, 4, 5, and 6. You’ve only got a limited number of coins available, so you may not exceed ten piles.

Iachimo will go first and you will take turns drawing coins from the piles. On your turn, you may remove as many coins as you like from any one pile. The winner is the one who takes the last coin and leaves his opponent without a move.

“Double or nothing,” he dares you, with a bit of desperation in his voice. You’re not sure what would happen if you decline. It doesn’t matter, though, since you see a clear path to victory, even allowing Iachimo to go first.

How many piles do you set up? What’s your strategy for winning?

Iachimo likes to hang out at the local tavern, drawing in tourists to play a game of Nim. You don’t like Iachimo. You don’t like him at all. You think he’s a huckster and a con man. You’d like nothing better than to beat him at his own game. You want to beat him at Nim.

In Nim, two opponents take turns drawing from several piles of coins. On your turn, you may remove as many coins as you like from any one pile. The winner is the one who takes the last coin and leaves his opponent without a move. The coins themselves are not on the line, but Iachimo likes to make the game more interesting with a modest wager.

As you enter the tavern, you notice that Iachimo is set up for business. He has stacked five piles of coins, numbered 1, 2, 3, 4, and 5. Each pile has the same number of coins as the pile number: 1, 2, 3, 4, and 5. He sees you coming and amiably offers you a friendly wager which you quickly accept.

“I’ll go first,” you smile, and before Iachimo can object, you make your move.

What’s your first move? What’s your strategy for winning?

One of my favorite pieces of trivia is that John Adams and Thomas Jefferson died on the same day. What’s truly remarkable about this is that it happened on July 4, 1826, which was the 50th anniversary of the famous signing of the Declaration of Independence. John Adams’s last words are reported to be “Thomas Jefferson survives” - he did not know that his long-time friend and rival had died a few hours earlier. For us, then, knowing that Jefferson died first is an essential part of the story of these great founding fathers.

But what of the founding fathers of Western literature? Recently, we celebrated April 23 as Shakespeare’s birthday, but we also know it as his death day. Shakespeare died in Stratford on April 23, 1616. We do not know the time of his death, or his last words.

Miguel de Cervantes, author of Don Quixote, might likewise be considered one of the founding fathers of Western literature. Cervantes died in Madrid on April 23, 1616. We do not know the time of his death, or his last words.

And yet, it is possible to say, with some degree of certainty, which of the two authors perished first. And that, dear readers, is today’s Conundrum.

Who died first: Shakespeare or Cervantes? How do you know?

Feel free to speculate as to last words too, if that sort of thing amuses you.

UPDATE: Question answered by Neel Mehta. See comments for answer.

Today is Shakespeare’s 444th birthday.

This means that if Shakespeare were alive today, he would be the world’s oldest human. In fact, he would be the oldest human who ever lived.

The number 444 makes me think of the Iran Hostage Crisis. The hostages were held for 444 days.

444 is a Harshad number. It is also a palindrome.

The year 444 AD was precisely 1564 years ago. What year was Shakespeare born? 1564. Believe it or not!

President Bush now has a job approval rating of 19 percent.

How bad is that? Even sugared gum was signed off on by one out of five dentists. That’s 20 percent.

His job approval is only 14 percent on the economy. The remaining 5 percent who gave him a thumbs-up overall must have been dazzled by the undeniably admirable job he’s been doing managing the Iraq situation.

Paul Krugman has a compelling post about the old canard that cutting taxes increases revenue. I’ve heard Giuliani spouting this line on the campaign trail, pandering to the Club for Growth crowd.

This seems to me to be a conservative fantasy, a cynical ploy to appeal to people who are so opposed to paying their taxes that they are willing to abandon the most basic logic. Surely we can all agree that if we cut taxes down to zero, then we will take in less revenue. Therefore, it must follow that there is a point beyond which cutting taxes cannot increase revenue.

I do understand the economics behind the principle. Cutting taxes leads to more disposable income for consumers, which leads to greater demand for goods and services, which leads to increased demand for labor, which leads to increased employment and wages, which creates more overall income to be taxed. However, in this age when outsourcing of labor is on the rise, and America is importing more goods than it is exporting, that chain seems to have a few weak links.

Yesterday on This Week, George Stephanopoulos cited a “stunning” statistic from the Congressional Budget Office:

From 2003 to 2005, the increase in income for the top one percent exceeded the total income of the bottom twenty percent.

Turn that over in your mind for a moment before we move on to the Question of the Week, which comes to us via the Hoover Institute, a conservative think-tank at Stanford University.

How much does the gap between rich and poor matter? In 1979, for every dollar the poorest fifth of the American population earned, the richest fifth earned nine. By 1997, that gap had increased to fifteen to one. Is this growing income inequality a serious problem? Is the size of the gap between rich and poor less important than the poor’s absolute level of income? In other words, should we focus on reducing the income gap or on fighting poverty?

It’s a fair point. Do rising waters raise all ships? And if so, does it matter if the rich get richer faster than the poor get richer? Or is income inequity really the problem, and a bigger slice of the pie for the rich means less for everyone else? And is it okay to mix ship and pie metaphors when talking about economics? I guess what I’m asking is this:

Does the income gap matter?

A game is considered to be “solved” when all of the possible moves have been mapped out in a mathematical tree and thus the perfect set of moves can be determined regardless of an opponent’s play.

Tic-Tac-Toe is a pretty easy one. You solved this as a kid. There are three opening moves - corner, edge, center. And then you work from there.

Connect Four was solved in 1988. That’s because those new-fangled computer thingies were starting to get some real power behind them. If you want to play Connect Four against the best opponent you’ve ever played in your life, check out the applet on John’s Connect Four Playground which is programmed to play flawlessly, based on a database of pre-determined best moves. But if you go first, and play just as flawlessly, you can beat it.

Checkers was solved this past April by researchers from the University of Alberta. You can play against Chinook, which will play flawlessly, but the best you can hope for is a draw. It doesn’t matter how amazingly good you are at checkers. You will never win. For me, there’s something a little disturbing about that.

Could chess be next? There are an incredibly large number of possible games, but it must be finite. And if it’s finite, then the tree must conceptually exist even if nobody has been able to come close to mapping it yet. Some see chess playing ability as intutive and creative, and not merely a number cruching process. But if number crunching continues to get better, it might evolve to the point where we get a chess-playing program as unbeatable as Chinook.

To be clear, we’re not talking about a really, really good chess-playing program. We have that now. We’re talking about a program that can access an exhaustive database of pre-determined best moves in order to ensure the most favorable outcome possible.

What do you think?

Will computers ever solve chess?

From the American Research Group:

November 13, 2007 - Impeachment

A total of 64% of American voters say that President George W. Bush has abused his powers as president. Of the 64%, 14% (9% of all voters) say the abuses are not serious enough to warrant impeachment, 33% (21% of all voters) say the abuses rise to the level of impeachable offenses, but he should not be impeached, and 53% (34% of all voters) say the abuses rise to the level of impeachable offenses and Mr. Bush should be impeached and removed from office.

The respondents didn’t specify whether they were specifically referring to the administration’s policy on torture. They didn’t say if they were talking about how they cherry-picked intelligence to justify a wrong-headed war, or how they compromised national security by outing a covert CIA operative, merely as retribution for her husband calling them on their lies. The respondents may not have been specifically responding to warrantless wiretapping and secret military tribunals. They may have simply been thinking of how the administration handed over all government regulation to the industries being regulated. The data doesn’t say. All they were asked was if President Bush abused his power, and 64% said he did. The data also doesn’t show what the other 36% were thinking.

When you look at the data, though, something else is striking.

I’m surprised, though I guess I shouldn’t be, that so few people gave Response 2. Imagine a graph of this data. Usually a distribution like this would slope up, slope down, or rise in the middle like a bell curve. That this data set has such a sharp dip in the middle is a testament to just how polarizing this president has been. 64% of Republicans feel that President Bush has not abused his powers as president at all, while 50% of Democrats feel he should be impeached for it.

Also, more than one-fifth of respondents in general felt that his abuses had risen to the level of an impeachable offense, but that he shouldn’t be impeached. Isn’t that being soft on crime? Or perhaps we just remember the last time an opposition Congress impeached a sitting president, and are unwilling to go through all of that again, even if it’s warranted this time.

Because for 36% of the population, warrants are sooooo 20th century.