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  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

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#43501 Re: Introductions » i hate subject fields. » 2005-10-12 16:37:44

Hi burrita,
Welcome to the forum.

#43502 Re: Guestbook » Austraila » 2005-10-11 20:27:37

I like Australia too.

australia-map.gif

#43503 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-11 20:22:13

Problem # k + 28

For any value of n (n∈N), prove that n²! is divisible by (n!)^n.

#43504 Re: Puzzles and Games » Make 28 » 2005-10-11 19:11:57

I don't know if its allowed:-
38 - (2 x 5)

#43505 Re: Help Me ! » algebra » 2005-10-11 16:36:21

Let the speed of Ben be x mph. Therefore, the speed of Alan is x - 0.6 mph. Their combined speed is 2x - 0.6 mph. This is equal to 11.4 miles divided by 3 hours. i.e.3.8 mph.
2x - 0.6 = 3.8,
2x = 3.8 + 0.6 = 4.4
x = 4.4/2 = 2.2
Therefore, the speed of Ben is 2.2 mph and the speed of Alan is 1.6 mph.

#43506 Re: Help Me ! » More Equations! » 2005-10-11 16:08:34

x = y + 30
y = 3z, z=y/3
Therefore, x + y + z = y + 30 + y + y/3 which is equal to 1500.
7y/3 = 1500 - 30 = 1470
y = 1470 x 3/7 = 630
y=630, x=660, z=210.

------------------------

Millie has 40 coloured shapes.

25 are circles and the rest are squares

23 of the shapes are blue and the rest are green

Therefore, 25 are circles and 15 are squares.

23 of the shapes are blue, therefore 17 are green.

The least number of blue circles is 8 and the least number of green circles is 2.

#43507 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-10 00:33:15

Problem # k + 27

What is the value of (1-Cos2A) / (1+Cos2A) given that tan A = 3/4 ?

#43508 Re: Dark Discussions at Cafe Infinity » Random Words » 2005-10-09 23:52:17


Serendipity

Osmosis

Catastrophe

Vigintillion

Connivance

Regicide

Thanatophobia

Mercenary

#43510 Re: Jokes » www.funcyber.com/good-free-jokes : joke site » 2005-10-09 18:00:19

The proper link is
www.funcyber.com/good-fun-jokes/.

Click here

I haven't seen the contents on the website yet, I have just provided the link.

#43511 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-09 16:48:15

Problem # k + 26

There are 2 brothers among a group of 10 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?

#43512 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-09 16:38:49

You are right Mathsy. The solution to the problem given was 81.5, which is certainly incorrect! I would solve the problem exactly the way you did
(I thought of the method of solving at the time of posting, but didn't actually solve it!)

#43513 Re: Introductions » Hi » 2005-10-09 16:32:59

I forgot to mention...I think Kylekatarn is from Portugal too smile

#43514 Re: Help Me ! » Perfect Square Proof » 2005-10-09 16:31:22

A simple proof I can think of is
(a+b+c)²=a² + b² + c² + 2ab + 2bc + 2ac
When n=1 in your case,
a=10000, b=200, c=1
The resultant is 100000000 + 40000 + 1 + 4000000 + 400 + 20000 = 104060401.
This will continue as n increases.
For example, for n=2,
a=1000000, b=2000, c=1.
The resultant would be 1000000000000 + 4000000 + 1 + 4000000000 + 4000 + 2000000 = 1004006004001.
It can be seen that the other digits are not affected because of the number of zeros in a and b.
Hence, for any value of n, the resultant is a perfect square.
q.e.d

#43515 Re: Introductions » Hi » 2005-10-08 17:40:20

Hi frol....
I have a special place for Portugal in my heart, because I spent most of my childhood in Goa, India, earlier a colony of Portugal.
Here are some pictures of Goa....
st-cathedral-church-goa.jpg

goa_bom_jesus_church.jpg

dona-paula-goa.jpg

beach-dona-paula-goa.jpg

goa-beaches-india.jpg

#43516 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-07 23:19:39

Problem # k + 25

Three mathematics classes: X, Y, and Z, take an algebra test.
The average score in class X is 83.
The average score in class Y is 76.
The average score in class Z is 85.
The average score of all students in classes X and Y together is 79.
The average score of all students in classes Y and Z together is 81.

What is the average of all the three classes?

#43518 Re: Help Me ! » Math Study Tips... » 2005-10-06 20:50:22

Understand the logic. Learn the techniques. Remember the formulae. Practice methods of proving. Most important, hone your calculation skills and never forget the fundamental concepts.
big_smile big_smile big_smile

#43519 Re: Help Me ! » help plz » 2005-10-06 20:39:22

Yes, very much British smile

#43520 Re: Help Me ! » help plz » 2005-10-06 16:13:35

In India,
y = mx + c
where c is the y intercept and -x/y is the slope (or gradient),
when written as y - mx - c = 0 smile

#43521 Re: Jai Ganesh's Puzzles » Problems and Solutions » 2005-10-06 16:03:32

Problem # k + 24

A cube is made by cutting off the excess portions of a sphere of radius r. What is the volume of the biggest cube that can be formed?

#43522 Jokes » Tips to improve your writing » 2005-10-06 00:06:21

Jai Ganesh
Replies: 13

1. Avoid alliteration. Always.
2. Never use a long word when a diminutive one will do.
3. Employ the vernacular.
4. Eschew ampersands & abbreviations, etc.
5. Parenthetical remarks (however relevant) are unnecessary.
6. Remember to never split an infinitive.
7. Contractions aren't necessary.
8. Foreign words and phrases are not apropos.
9. One should never generalize.
10. Eliminate quotations. As Ralph Waldo Emerson said, "I hate quotations. Tell me what you know."
11. Comparisons are as bad as cliches.
12. Don't be redundant; don't use more words than necessary; it's highly superfluous.
13. Be more or less specific.
14. Understatement is always best.
15. One-word sentences? Eliminate.
16. Analogies in writing are like feathers on a snake.
17. The passive voice is to be avoided.
18. Go around the barn at high noon to avoid colloquialisms.
19. Even if a mixed metaphor sings, it should be derailed.
20. Who needs rhetorical questions?
21. Exaggeration is a billion times worse than understatement.
22. Don't never use a double negation.
23. capitalize every sentence and remember always end it with point
24. Do not put statements in the negative form.
25. Verbs have to agree with their subjects.
26. Proofread carefully to see if you words out.
27. If you reread your work, you can find on rereading a great deal of repetition can be avoided by rereading and editing.
28. A writer must not shift your point of view.
29. And don't start a sentence with a conjunction. (Remember, too, a preposition is a terrible word to end a sentence with.)
30. Don't overuse exclamation marks!!
31. Place pronouns as close as possible, especially in long sentences, as of 10 or more words, to the irantecedents.
32. Writing carefully, dangling participles must be avoided.
33. If any word is improper at the end of a sentence, a linking verb is.
34. Take the bull by the hand and avoid mixing metaphors.
35. Avoid trendy locutions that sound flaky.
36. Everyone should be careful to use a singular pronoun with singular nouns in their writing.
37. Always pick on the correct idiom.
38. The adverb always follows the verb.
39. Last but not least, avoid cliches like the plague; They're old hat; seek viable alternatives.

#43523 Re: Dark Discussions at Cafe Infinity » Wink Murder 4 » 2005-10-04 23:15:39

justlookingforthemoment wrote:

Playing
justlookingforthemoment
MathsIsFun
Mathsyperson
Zach
insomnia

Ganesh may be added to the list smile

#43525 Re: Help Me ! » combinatorics in playing cards - 52 caard standard deck » 2005-10-04 23:08:43

I think the required probability is

(32 x 28 x 24)/(52 x 51 x 50) assuming the raminaing two cards can be either paired or unpaired, greater or lesser than nine.

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