Math Quiz

[Capn]

26
|
2*13

well ok, I'm done

 

[chess9]

CapN: Awesome! That's almost right. Actually, 26 is the only number juxtaposed between a square and cube root. No other number has that quality. My thanks to Fermat for this interesting bit of math trivia.

Fermat is best known for his Last Theorem and the travails of Andrew Wiles in solving it, mentioned by CapN. But he was one of the foremost mathematical thinkers of his age and perhaps among the top 10 ever. He made numerous mathematical proofs, including the proof for this one. See Simon Singh's Fermat's Enigma. Also, PBS ran a special on Wiles two years ago. If you get a chance to catch the re-run, do so. It is a remarkable story of human courage and perseverance.

For those who don't know or remember, Fermat's Last Theorem states that x to nth power, plus y to the nth power, never equals z to the nth power where n is any number greater than 2. This is an obvious, and quite tricky, variant of the Pythagorean Theorem. Many mathematicians failed to solve the problem, until Wiles devoted his life to the problem and announced the solution in 1993, only to discover to his horror, after the announcement, that it was wrong! After a year of near torture he finally corrected his mistake and solved the problem!

 

[Duckers]

1001! = 4.02789647337170867317246136357e+2570, I assume there are 0 consecutive 0's or infite if you wanna definite it as 1001!.000000(infite)

log26 = almost the square root or 2 ?

 

[Duckers]

Oops, I didn't notice it was already solved!

 

[chess9]

MisterT: I'd guess an infinite number or none, at first blush.

 

[Capn]

I'm in chess' camp on this one, capn says none too.

 

[chess9]

MisterT: Would that be an irrational number?

 

[chess9]

By the way, I'm no math genius or expert. I minored in Math. But I do love math problems, riddles, and trivia.

MisterT: Yes, I heard about that Indian fellow. Isn't he the only person to get a PhD. from Oxford in math without the benefit of any undergraduate degree? Unfortunately, when he went back to Inja he was never heard from again!

 

[Mister T]

Duckers

How may consecutive zero's at the end, not how many digits total.

 

[Capn]

I'm still saying none, explanation? Because....

Actually, no wait uh 2 yah that's it

 

[chess9]

Wouldn't one zero be sufficient?

 

[Viper Frag]

Hey Capn stop taking all the credit. I came up with the factor tree.

 

[Viper Frag]

There is one 0.

 

[chess9]

Viper: Yup, you made the big breakthrough. Good thinking!

 

[Mister T]

ok 1001 ! (factorial) is the product of all integers between 1 and 1001 inclusive. Therefore it cannot be irrational. The product of any integers, by definition, cannot be irrational.

Since 1001! is finite, it cannot have an infinite number of zero's.

Also, since it is the product of all integers between 1 and 1001 inclusive it MUST have at least 2 since 10! yields 3,628,800.

About Ramanujan. Chess9 you are correct. He died because of malnutrition for some insane religious beliefs. While he was
in England he virtually ate no food which caused him to become very
sick after a while. What a pity.

 

[chess9]

MisterT: Very interesting. Makes sense, though. Too bad about the Indian. I assume he was a Hindu or Zoroastrian? Did the Z's worship numbers? Would have been perfect for him!!!!

 

[Capn]

Mister T, I got as far as figuring out 10! was equal to 3,628,800 as well and pluggin in some numbers. For the small numbers that I actually tried it was 2 for most cases, unless the number you multiplied it by was divisible by 5. In that case (being that the number you multiply by, is divisible by 5) there are three 0's. Since we are multiplying (1001!/10!) a number surely divisible by 5, I must revise my guess a third time and say there are 3 0's

 

[graen drol]

2097?

 

[chess9]

MisterT: 10 x 2 zeroes would be 20 zeroes. That's my final guess. I'd use Mathematica for that one!

 

[Mister T]

Capn
You are on the right track. However the answer is not 3. With 20! you get 4 zeros by the way. We are looking for 1001!.

graen drol

You are off by about 1 order of magnitude

chess9

20? nope you are also off by 1 order of magnitude

 

[Capn]

200

 

[chess9]

MisterT: Ok, 200? Yes, Regis, that is my final answer.

 

[graen drol]

333?

 

[BA]

I spent many of my middle school days in various math contests, so I already knew how to do this. It's not 200, although that's getting close.

Mister T, can I tell them the answer?

 

[Duckers]

is 200 the answer ?

I used this analogy which is likely to be wrong:

if 10! has 2 zeros and 20! has 4 then we can see that 10/2 = 5 and 20/4 =5 so I figured that 1000/200 = 5.

Is 200 the right answer ?

I see that Chess and Capn also figured the same number...