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#226 Re: Introductions » Hi all » 2010-01-21 06:40:28

Promoting Cuban cigars, are you?

#228 Re: This is Cool » A silly prime number method. » 2010-01-18 20:47:43

I take it you have not heard of the sieve of Eratosthenes.

#230 Re: Help Me ! » Chances of getting tail on a coin before 1 on a die? » 2010-01-16 14:00:57

I was assuming that the die was rolled simultaneously with the flipping of the coin.

#233 Re: Exercises » What do you think? » 2010-01-15 04:50:39

Yes, of course.
should be 11.75. (9.75 is what both sides of the equation should be equal to.) Sorry, got confused.

#234 Re: Exercises » What do you think? » 2010-01-15 02:44:07

bobbym wrote:

An urn contains 15 balls. There are only 2 different colors the balls can have, red and orange. There are at least 3 of each color in the urn. Picking 3 balls without replacement. the probability that all of the picked ones are red is the same as the probability that exactly one of them is orange. How many of the 15 balls are red?

Suppose there are n red balls (
). The probability of picking 3 red balls is
. The probability of picking exactly one orange ball is
. Hence, if they are equal, we have
.

#235 Re: Jokes » Puns » 2010-01-13 02:21:46

soroban wrote:

.



. .


. .


.

That’s quite funny. lol I think there’s a slight typo though. What the narrator said was “deaf in two ears” (which the other person misheard as “dead in two years”).

#237 Re: Puzzles and Games » Billiard Tables » 2010-01-10 00:08:09

Fruityloop wrote:

JaneFairfax,
   Absolutely amazing!  Your scores and times verge on being unbelievable!  Hmmm... is there a connection between number theory and being skilled at billards?

sign0092.gif

When playing any game, you have adopt a specific strategy based on that particular game. For this one, my tips for getting to 2501 or highter would be these:

(1) Go for the highest-scoring pockets.
(2) Go for the most accessible pockets and pot as quickly as possible.

(1) Obviously going for high scores such as 12 × 12 = 144 will advance your total score much more quickly than if you only try low scores like 2 × 2 = 4 (which you would have to do 36 times before your total score advances by 144). However, in some of the table configurations, the highest-scoring pockets may be rather inaccessible. In this case, (2) might be a better option. For instance, suppose the pocket marked 12 on a particular table is in a tricky corner, and it might take you 30 seconds to make a successful pot there. Then you would take one minute to make 12 × 12 = 144. On the other hand, there may be a pocket marked 9 on the same table where you can pot successfully in just 10 seconds. If you go for that pocket four times, you would score 162 in 40 seconds – more points in less time than going for the awkward pocket marked 12.

Try and strike a balance between (1) and (2) to get to 2501 as quickly as possible.

#240 Re: Help Me ! » simple groups » 2010-01-08 14:59:15


Are you familiar with the theory of group actions? All Sylow p-subgroups of a group
are conjugate, so if
is the set of all Sylow p-subgroups, then
acts on
by conjugation and for any
the number of Sylow p-subgroups is the size of the orbit of
under this action. By the orbit–stabilizer theorem, the size of the orbit of
is the index in
of the stabilizer of
in
, and the stabilizer of
in
is easily seen to be the normalizer of
in
.

For Humphreys’s corollary, see this: http://www.mathisfunforum.com/viewtopic … 38#p109938.

#241 Re: Help Me ! » Primes » 2010-01-08 00:40:22


Because the list of numbers
for
does not exhaust the list of natural numbers. It just gives you finite sequences of
consecutive non-primes. There will always be gaps between the finite sequences where prime numbers can fit in.

For example,

gives the sequence
and
gives the sequence
. You can see that there is a big gap between 9 and 26 where prime numbers can be found.

#242 Re: Help Me ! » abstract algebra problem(groups, rings) » 2010-01-07 11:22:43

Hint for #1:

Let

be a finite subgroup of
where
and
. Set
. Now show that
.

#244 Re: Exercises » What do you think? » 2010-01-01 13:16:03

bobbym wrote:

Hi;

Try this one on for size, it is quite easy. Which is larger and why?

#245 Re: Guestbook » Fbi » 2010-01-01 12:58:15

Wow that is cool.

#246 Re: Exercises » Is this cool with you? » 2010-01-01 03:47:27

bobbym wrote:

A person reduces the assertion that there is always a square between n and 2n inclusive for all n to this inequality:


That would be looking for a square between
and
. It does not imply that there is a square between
and
.


Correct proof of #3.

If the statement were false, there would exist a natural number

and a natural number
satisfying

With some simple algebraic manipulation, we should arrive at

It can be easily checked that there are no natural numbers

satisfying
for
or
and so we have a contradiction.

#247 Re: Exercises » Is this cool with you? » 2010-01-01 03:34:48

bobbym wrote:

Hi;

How would you judge this answer? And why?

rotfl.gif rotfl.gif rotfl.gif

#249 Puzzles and Games » Billiard Tables » 2009-12-30 11:02:17

JaneFairfax
Replies: 14

http://www.mathsisfun.com/games/billiard-tables.html

The object is to score 2501 points or more. I completed the game in under 10 minutes.

BilliardTables.png

#250 Re: Exercises » Fumble and Botch strike again. » 2009-12-28 04:56:35

There is nothing wrong with mods; I use them a lot too. But I also like to keep my mind open for simple solutions, if they exist. smile

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