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#1 Re: Help Me ! » probability » 2011-12-05 05:02:25

juantheron wrote:

Let A = {0,1,2 ..... 9}

how many  different 4-digit number that is divisible by 3

if number is choosen from set A

lookagain edit wrote:

Let A = {0,1,2 ..... 9}

How many  different 4-digit numbers are divisible by 3
if each digit is chosen without replacement

from set A, and 0 cannot be a leading digit?

For each of the following, there are potentially 4! permutations,
except that 0 cannot be a leading digit, so 3! permutations
must be subtracted.  So multiply each of these representative
numbers by 18 to get the total number of permutations for
this partial group:


18(15) = 270


For this second (last) partial group,
the number of permutations for
each representative number is 4!
Then multiply by 24 to get the total
number of permutations for this
partial group:

















24(39) = 936

Grand total
270 + 936 = 1,206

#2 Re: Maths Is Fun - Suggestions and Comments » The checkers game plays with poor strategy. It's basically ... » 2011-12-05 01:43:36

I don't know if this javacsript, at this address:

Scroll down to the checkers option.

10 levels 

Play against the computer.

You or the computer can start.

Levels 9 and 10 may keep a player waiting for several
seconds, depending on the complexity of its move
at the time.

#3 Maths Is Fun - Suggestions and Comments » Issues with the inverse functions page » 2011-11-25 18:38:20


"Not Always Solvable!

It is sometimes not possible to find an Inverse of a Function.

Example: f(x) = x/2 + sin(x)

We cannot work out the inverse of this, because we cannot solve for "x":

y = x/2 + sin(x)

y ... ? = x"

This function isn't even one-to-one, so by default, a person cannot
find an inverse for it, because the inverse does not exist for it.


Also, you could mention that certain functions are inverses of themselves.

#4 Maths Is Fun - Suggestions and Comments » Sufficient condition left out about parallel lines » 2011-11-25 17:49:48


"Parallel Lines

How do you know if two lines are parallel?

Their slopes are the same!"

The lines must also have different y-intercepts, else they are the
same line.

So, if you know that their slopes are the same, then you don't
(automatically) know if they are parallel lines or not.



On parallel vertical lines:

"a vertical line is parallel to another vertical line."

No, for example, x = -2 is a vertical line, and

3x + 6 = 0 is another vertical line.  These lines
are not parallel to each other because they are the
same line.

Distinct vertical lines are parallel to each other.

#5 Maths Is Fun - Suggestions and Comments » The checkers game plays with poor strategy. It's basically ... » 2011-11-25 17:37:08

showing how to lose by playing so poorly with its strategy.

It promises:

"Checkers - Practice here, then obliterate your friends   Play » "   

I do like:

1) the looks of ithe board and pieces
2) how to click the pieces to move
3) the speed at which it returns a move
4) apparently it plays by the correct rules of checkers/draughts


Can you amend it or substitute it with a different
computer checkers game to improve at least
novices' skills, please?

#6 Re: Maths Is Fun - Suggestions and Comments » Parallel and Perpendicular Lines and Planes » 2011-11-25 16:59:00

MathsIsFun wrote:

A new page for your enjoyment: Parallel and Perpendicular Lines and Planes

Comments, suggestions welcome.

Click onto this link for the problem (mind bender) at the bottom of the page.

"Mind Bender
Something that makes my mind bend: we know that if we have two parallel lines,
and we rotate one by 90°, they will be perpendicular to each other, right?
Well, does the same apply to curves? Can you have "perpendicular curves",
by rotating one of them by 90°? I simply don't know, but it is fun to think about."


Let there be two racetrack-shaped closed curves,
not necessarily the same width or length, having
semicircles at each end facing out and each semicircle
is connected by parallel lines to the endpoints of the
respective semicircles.

Let these two curves be oriented parallel to each other,
have sufficiently long line segment sides to connect
the semicircles, and be positioned relative to each other
so that when one is rotated 90 degrees, there will be
either two intersection points or four intersections where
the intersecting sides will be perpendicular to each other.

Before the rotation of 90 degrees, there are cases where
one of these "racetrack" curves might even be completely
inside of the other.

#7 Help Me ! » bobbym, you are being reported to the administrator. You're not... » 2011-11-25 06:03:36

allowed to be a tyrant on the forum, just because you make false claims about
I have typed.

This is going to stop of yours.

#8 Re: Help Me ! » exponential limit » 2011-11-25 04:30:51

bobbym wrote:

Some of the of the conspirators were hung,

They were hanged. And I already mentioned that in the previous

What's worse than making the error the first time with the other
poster is to repeat it a second time.

#9 Re: Puzzles and Games » Useless parent puzzle » 2011-11-24 20:36:27

Ozyhibby wrote:

Help- if you were numbering hotel room doors 1-2012 how many of each number (ie 1-9) would you need.



Ozyhibby wrote:

It's not for me.  Trying to


my niece with homework.

I'm afraid maths is not my strong point.

#10 Re: Help Me ! » exponential limit » 2011-11-24 20:23:01

bobbym wrote:

Hi bob bundy;

If you come at it from the left it will approach 25.

If you come at it from the right it is complex but the still
approaching 25 because the complex part of the argument is going to 0.

"Along with other conspirators he was [hanged], drawn and quartered."

People are not hung, unless possibly, they are literally placed on a hook
on a wall (or similar) as a picture frame would be.

#11 Re: Help Me ! » inequality » 2011-11-23 14:00:31

bobbym wrote:


Possibly one side should be

#12 Re: Help Me ! » gcd » 2011-11-22 19:41:22

jacks wrote:




As a consequence, where an n value works, it must be even,
because n^2 + 1 and n^2 + n will be even when n is odd
and hence divisible by at least 2.

Whenever n^2 + 1 is a prime (greater than 2), then that n is a solution.

It is not known whether there are an infinite number of primes
of the form n^2 + 1.


If n^2 + 1 equals certain composite composite numbers, then it
is possible for the gcd = 1 for those certain cases.

An example is n = 8.  Then n^2 + 1 = 65 (composite)
and n^2 + n = 72, which is also composite, but the
gcd(65, 72) = 1 and therefore n = 8 works.

#13 Re: Dark Discussions at Cafe Infinity » Spelling bees aren't run fairly. Too much variability in the ... » 2011-11-21 02:45:32

Monday, 11/21/11

Administrator of MathIsFun:

Problem:  spamming by bobbym

I already sent a message intended for you to lock this
thread that is located here


Please do it now, and it is my thread that I
started anyway.  It has been hijacked by bobbym,
who keeps spamming it with posts of lies towards me.

Thank you,

User reconsideryouranswer

#14 Re: Dark Discussions at Cafe Infinity » Spelling bees aren't run fairly. Too much variability in the ... » 2011-11-21 01:56:45

bobbym wrote:

That is Kasparov's opinion, and it is not a statement of fact.

Try to understand that everything you have said is also opinion.

You feel that there is variability in the test.

[math\text{Your statement is utter presumptuous, and therefore}[/math]

So unless you can get on the school board...

[math\text{It is similar to saying that one be a checf to know that the food doesn't taste good.}[/math]

I was not vague because you could not understand the reference.
You must begin to accept the fact that you might be wrong.
Your opinion does not qualify as a fact. Thousands of kids have
taken and will be in future spelling contests.
They are satisfied with the rules and the results, why aren't you?

However, the total number of losses due to unluckiness of
the words given to them increases on average with the newer totals
of spelling bees conducted.

Unluckiness? First you say more spelling bees would reduce the luck factor ( which is true )
now you say it does not.

Sorry, in competition which you do not want to admit a spelling contest is, nerves and luck counts.
You are still holding on to the opinion that the losers were unlucky. That they were superior spellers
but were somehow discriminated against.
[tex]Random difficulty of words **is** dicrimination, so accept that.}[/math]

You say you are not but everything you say proves otherwise.

The words are picked carefully to be of equal difficulty.

Even if they were not, the best spellers would still win.

Remember I missed on very, very easy words, my opponents did not.

If I remember the next contestant spelled my word correctly.

To be edited . . .
Now what the heck is unfair about that.

#15 Puzzles and Games » True-false exercises in mathematics and other areas » 2011-11-20 07:23:08

For the true-false problems for this thread, all cases for a particular
statement must be true, else it is deemed false. That is, I am not
presenting exercises in the always true/sometimes true/never true format.

1. Within the confines of the United States, the westernmost part of Virginia
lies farther west than the westernmost part of West Virginia.

Suppose there are sets of fair, 6-sided dice, but they do not necessarily have
the values of 1 through 6 once each on each face.  Numbers other than
1 through 6 might be included, as well as certain sides could share the
same value.  An example might be a die with these values, one per each face:
2, 2, 3, 4, 5, 8.  The value of two or more dice thrown, such as A + A, is the sum
of the values of their top faces.

There are also sets of C dice and D dice with the above properties.
Dice X, Y, W, and Z are also like the above in properties, except that
they are nonspecific for the illustration below.

Given: One set of four fair, identically-numbered 6-sided dice and a different
set of four fair, identically-numbered dice.  X > Y means that die X
has a greater chance of having a larger value than die Y upon tossing them.
W < Z means that die W has a greater chance of having a smaller value
than die Z when the dice are tossed.

2. (i)

If A > B, and A + A  + A > B + B + B, then

A + A > B + B.

2. (ii)

If A + A < B + B and A + A + A + A < B + B + B + B, then

A + A + A < B + B + B

2. (iii)

If A + B > C + C, and A + B > D + D, then

A + B > C + D

"Lines" in the following refer to straight lines in the xy-plane.
Also, I am using "asymptote(s)" here to be only lines
(horizontal, vertical or oblique) instead of the nonlinear
asymptotes that exist for other certain functions.

3. (i)

Given:  A certain function approaches a line and gets ever closer
to it without intersecting it. 

That line is an asymptote to that function.

3. (ii)

A function does not interect its asymptote(s).

3. (iii)

The same function cannot have a horizontal asymptote
and an oblique asymptote.

4. In the vertical line test, where there is a graph of a relation
that is not a function, the vertical line crosses at two or more
points for each corresponding x-value in the relation's domain.

5. For any pair of perpendicular lines, the value of one slope
multiplied by the value of the other slope equals -1.

6. In plotting three points for a certain intended line (on graph paper,
for example) in the xy-plane, if a person has three points
that line up, then that person knows that those three points
lie on the same intended line.


8. There is a movie starring Jim Carrey and Kate Winslet
involving erasing of certain memories.

The title of this movie is one of the choices below, true or false:

"Spotless Mind of the Eternal Sunshine"

"Spotless Eternal Sunshine of the Mind"

"Spotless Sunshine of the Eternal Mind"

"Spotless Eternal Mind of the Sunshine"

"Eternal Spotless Mind of the Sunshine"

"Eternal Spotless Sunshine of the Mind"

"Eternal Mind of the Spotless Sunshine"

"Sunshine of the Spotless Eternal Mind"

"Sunshine of the Eternal Spotless Mind"

"Sunshine Eternal of the Spotless Mind"

"Sunshine Spotless of the Eternal Mind"

"Mind of the Eternal Spotless Sunshine"

"Mind of the Spotless Eternal Sunshine"

"Mind Spotless of the Eternal Sunshine"

"Mind Eternal of the Spotless Sunshine"

9.  In the same plane, two distinct quadrilaterals can intersect
each other in no more than eight distinct places.

10.  There are no infinite subsets (all members distinct) of the set
of irrational numbers such that they can be put into a one-to-one
correspondence with the set of positve integers.

11. Given: a, b, c, d belong to the Real numbers, where a, b, c, d > 1.

12.  A polyhedron exists that has seven edges.

#16 Re: Dark Discussions at Cafe Infinity » Spelling bees aren't run fairly. Too much variability in the ... » 2011-11-19 17:47:47

Suppose that there is a more knowledgeable speller (and who works
well under pressure while spelling) among a particular set of contestants.

If a large enough number of spelling bees were to be conducted
using these same contestants, but no others, then the Law of
Averages would have the better seller winning most of the
spelling bees, despite the significant variability in the difficulty
level of the chosen words.

But, that doesn't apply, because the same sets of contestants
don't play each other in subsequent bees.

As it is, each new word  for an individual is similar to a coin flip.
On one side of the "coin," it could represent the contestant
getting a word of difficulty level near the that spelling bee's average
difficulty level of words.  Or, on the other side of the "coin,"
it could represent that contestant getting a word significantly
less difficult or more difficult than the average for that particular
set of contestants in that particular spelling bee.

#17 Re: Dark Discussions at Cafe Infinity » Spelling bees aren't run fairly. Too much variability in the ... » 2011-11-19 16:50:55

bobbym wrote:

You meant heck right?

What, is your crack supposed to dismiss it?

A statement is not a crack. That is you putting your
own spin on my thoughts.

A statement can be a crack, and regardless that you stated that
a statement is not (read:  is not equivalent to) a crack,
that makes your sentence, about a statement about not being a
crack, immaterial. 

And are you going to now deny that that statement was made to
discredit the Internet quote as to being taken seriously,
else you just rambled and went off on a tangent by typing it?
Either it was a crack to *attempt* to discredit the quote or it
was made in jest to change the subject.  Pick one.

where students are expected to act civil and be good role models
from the schools they are from.

You are describing an exercise in etiquette, not a contest. Contestants
must obey the rules, nothing more.

Of course the cleverest ones will bend them as much as possible.
This helps insure victory.

What is "got the job done?"  Better (and including fairer) ways come
along and show how the older ways were too flawed.

It means was adequate for the purpose.

One of those old and unfair statements that were before your time.


"Well, how do you know it got the job done?"

"It was because it was adequate for the purpose."

"How did you know it was adequate for the purpose?"

"Well, it got the job done."


It worked is my point! This is an attribute that it has and

your way lacks.

After all, your ideas have never been tested.

Is it possible that your ad hoc ideas are incorrect?

Garik Kasparov Former World Chess Champion wrote:

It is all the same
( contests of any kind ). The goal is to destroy the opponents ego, his will.

That is Kasparov's opinion, and it is not a statement of fact. 

The difference between a boxing match, basketball game or a spelling
contest is only the rules. The point is exactly the same.


A little probability will tell you that the luck you speak of averages out.

There is very little luck factor in a spelling contest ( old rules ).

You are in error assuming that the losers were unlucky.
They were outspelled, simple as that.

There are the cases where the  losers might/may have been
outspelled on words of similar familiarity/difficulty level and/or
got too nervous in their attempts on stage.

#18 Re: Help Me ! » Finding points of inflexion? » 2011-11-19 14:16:05

Annasophia wrote:

For the curve y = (x)/(x^2 + 1)

Show the points of

occur when x = 0, ±√3.

I can't find a spelling for "inflexion."  You can use "inflection" instead.

#19 Re: Dark Discussions at Cafe Infinity » Spelling bees aren't run fairly. Too much variability in the ... » 2011-11-18 09:27:57

bobbym wrote:

Our purpose is to help students improve their spelling increase
their vocabularies, learn concepts, and develop correct English usage that will help them
all their lives.

Sounds like an Oprah or Phil quote.

Good for the tv audience. That is like saying we have a presidential election to teach
the candidates good sportsmanship!

The purpose of contests is to win with lots of bloodshed for the spectators.

Watching each defeated kid leaving the stage with that look of utter despair that is
what interests the spectators. Holding up that trophy while glaring at the vanquished
that is what interests the competitors.

It does not matter a *flip* what you claim what the audience likes regarding it! 
The interests of the spectators is immaterial.  The competition isn't for them.
The competition is not for the audience, but for the contestants.
Is that another point that got by you?

The competitors can hold their trophies *regardless*.

The old time format of spelling contests got the job done!

The thrill of victory and the agony of defeat so to speak.
I know all about, "everyone is winner," "we are all unique flowers," "
it is not whether you win...," all the modern psycho-socio-babble.

It's more of a c-r-a-p-s-h-o-o-t as it is now run (and has been running)

One more thing, the best will always tell you that they make their own luck.

Nope, your premise is wrong to begin with, because there is no
"best" in this context where they aren't challenged on the same words.

All the ones I was in the best man won.

luck, was a significant factor which was not "made" by them.

#20 Re: Help Me ! » Help me please guys ... ! » 2011-11-16 16:39:27

RauLiTo wrote:

I have to answer these questions as an assignment ... Please guys try to help me as much as you can !

Thanks in advance !



your request is unreasonable.

This is not an assignment/homework-doing site, especially
some long list of multiple-part problems.

And the main thing is that you show your own work here for any given
problem first.

#21 Re: Dark Discussions at Cafe Infinity » Spelling bees aren't run fairly. Too much variability in the ... » 2011-11-16 16:33:24

bobbym & lookagain edit wrote:


No insult intended but did you just get eliminated?

Spelling contests, like all forms of competition are a test of what a person has under the hood.
They test, courage, stamina,

willpower, concentration, nerves and the desire to win.

They test, courage, stamina, luck, willpower, concentration, nerves and the desire to win.


Your attempts to create parity among the competitors is
defeating the purpose of the contest.

#22 Dark Discussions at Cafe Infinity » Spelling bees aren't run fairly. Too much variability in the ... » 2011-11-14 17:39:18

Replies: 11

spelling difficulty of the words is the prime factor.

All spellers should have to spell the same word during
the same round, at the same time, using magnetic
letters on a board (or something similar), in privacy
spaces (but facing out to the judges), and reveal their
spelling attempts all at the same time.

The ones who pass move on to another round.

There could be a double elimination to keep
players longer for another chance.

In the event that all of the players miss a
word on a reveal, they could be backed up
and retry on a different word.

The whole system (tweaks and all) would
cut down significantly on the variability of
the difficulty of one word for a person to
the next word for a different person.

#23 Re: Dark Discussions at Cafe Infinity » e » 2011-11-14 16:57:23

bobbym wrote:

How about the first 100 digit prime? It is found at position 346 and is ( drum roll )

15108657463772111252 3897844250569

Your display of the digits of the prime number got cut off.

#24 Re: Dark Discussions at Cafe Infinity » In part, bowling scores should be based on the number of strikes total » 2011-11-14 16:51:07

bobbym wrote:


perfect sense
to score
consecutive strikes as they do.

No, it's not to me.

Hypothetically, a bowler could get three (or four?) strikes in a row in the
first three (or four ?) frames and then get all gutter balls, showing he
can't maintain.  Not only are the points in his frames inconsistent,
he "goes downhill" to 0 on the gutter ball and stays there for the
remaining frames of a game.

While another bowler could throw five strikes about evenly spaced out,
with gutter balls in between, and score less than the previous player.
The points in his frames would have a closer to symmetric form
(a greater relative consistency), and he wouldn't be suffering from a
downward trend of decreasing strikes.

It'd be similar to a student answering the first 3 (or 4?) questions
on a 10 - 12 item multiple-choice quiz correctly (and the rest wrong)
and being awarded more points (a higher grade) than a student
who would get 4 to 6 questions correct in total.  And these would
be about evenly spaced out as possible for the questions which
were marked correct.

And, across 3 consecutive games (max. total of 900 points), the
first bowler could bowl 5 strikes in the first 5 frames, and 5 gutter
balls in the last five frames in the first game.  And then bowl 4
strikes in the first four frames with 6 gutter balls in the last 6
frames.  And in the third (last) game, that bowler could throw 3
strikes in the first 3 frames, with 7 gutter balls in the last
7 frames.

In contrast, the second bowler could bowl more strikes than the
first bowler did in his respective games (the rest gutter balls),
but spaced out with a lower official bowling score per respective
game.)  Not only would the second bowlwer be getting more strikes
than the first bowler in each game, but the first bowler's performance
would be getting worse with each successive game.

#25 Re: Help Me ! » sgn(x)!!! » 2011-11-12 13:10:15

anonimnystefy wrote:

i was wondering what derivatives of |x| and sgn(x) are.
i thought of something but i got that they were sgn(x) and 0
respectfully.i think something is wrong here.What?

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