John. H. Conway, one of the young men pictured above, tells us about his fabulous and simple method for rapidly calculating the day of the week.
With just a little practice, you too can Impress your friends (or drive them away) with this stupendous ability!
Save Indiana, his girlfriend, his father and his father’s sidekick from certain doom! They must cross a bridge across a gorge in no more than one hour!
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Niclas Hedell gives his solution to the third tree puzzle he posed last week, and we ask a puzzle about sums of numbers.
Niclas Hedell, a listener, poses a problem from his days in the Swedish military: given two trees in the forest, and a rope twice as long as the distance between the trees, how do you find a third tree so that all three make a right triangle.
And we explain how the Stork can catch the Frog.
Amusingly, this problem has exactly the same solution as the proof that there are as many rational numbers as there are counting numbers. And the proof generalizes: one stork can catch three frogs, or ten or fifty.
Here are some bonus problems:
Lord Butler, Knight of the Garter, has never heard of the rule on last week’s show. But he notes he does move down the table each year…
When we posed this problem, we thought things would turn out a little differently, as we discuss here.
The twenty-five members of the Royal Order of the Garter, founded in 1348, by King Edward III, dine once each year at Windsor Castle, about a round table. From time immemorial, there has been a rule that no two members may be seated next to one another more than once each decade. But can they do better?
A contestant for our Million-Dollar-Give-Away sent in Rayo’s Number, hitherto the largest number ever used for any real purpose: to wit, winning the
Check out the article by Scot Aaronson that inspired them to duke it out! And this thread on the math forum is quite interesting as well.
Graham’s number, as huge as it is, can be “described” or “named” in a very few symbols. Several people sent us programs that (in principle!) calculate Graham’s number— you can think of any of these programs as notation for Graham’s number.
Graham’s number is truly, absolutely staggering…
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