First, let’s answer last week’s puzzle on clocks!
As it turns out, there are 143 times in each twelve hour period for which you can switch the hands of a clock and still have a legitimate time! It’s easy to find these by plotting the positions of the hands throughout the day:
Steve D. wrote us to say:
I was listening to another podcast and they misread the copy and ended up
saying “What is the most numerous number?”. Well, what IS the most numerous number?
This is really a fascinating question! Have you ever wondered, for example, why there are 7 of so many things:
Really, it’s not that big of a mystery. The fact is, small numbers are very useful, and get called upon a lot. But there aren’t that many of them to go around.
Hence, the First Strong Law of Small Numbers: There aren’t enough small numbers to meet the many demands placed upon them!
The most numerous numbers, in a sense then, are the small ones. Google searches seem to confirm this:
Lotsa fun can be had in this way… With a little fishing, you can find some ridiculously large numbers with more hits than they deserve, but the principle is clear.
This same principle, incidentally, explains why, for example, the Golden Ratio appears in so many settings. There’s nothing really that mystical about it. The Golden Ratio is a root of the polynomial x2-x-1=0. Roots of polynomials come up all over the place, in countless applications. And just as small numbers are in great demand, roots of simple polynomials will appear over and over again.
The Golden Ratio is just about the simplest non-integer root possible, and so, of course, shows up endlessly.
Challenge Question I’m kind of curious now: What is the smallest counting number that is NOT on the web?
210210876 was not on the web until just now, according to Google. Internet history has just been made!! But I’m sure you can find something smaller…
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!
Read the rest of this entry »
Niclas Hedell gives his solution to the third tree puzzle he posed last week, and we ask a puzzle about sums of numbers.
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…
We never did resolve the question of which grows faster:
In this corner we have
Sequence 1 n^^n
1, 2^2, 3^3^3, 4^4^4^4, and so on.
And over here we have Sequence 2, defined recursively by
In short, we can define the second sequence as s(1) = 1; s(n) = n, followed by s(n-1) factorial signs.
Which sequence grows faster than the other??
We have many conflicting answers, and no decisive resolution; here was one idea .
Our minds boggle as we continue our quest! This week we discuss the Knuth Arrow notation, for describing some really staggeringly large numbers. And yet we are still two weeks from talking about the largest number ever used for any real purpose!
We also discuss an April Fool’s paradox! Last week we said there were three errors on the Math Factor. But there were only two, so this announcement was one of the three errors! But then the announcement was correct! ETC.
Download a great math factor poster to print and share!
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