You are not logged in.
Hi burrita,
Welcome to the forum.
I like Australia too.

Problem # k + 28
For any value of n (n∈N), prove that n²! is divisible by (n!)^n.
I don't know if its allowed:-
38 - (2 x 5)
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.
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.
Problem # k + 27
What is the value of (1-Cos2A) / (1+Cos2A) given that tan A = 3/4 ?
Serendipity
Osmosis
Catastrophe
Vigintillion
Connivance
Regicide
Thanatophobia
Mercenary
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.
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?
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!)
I forgot to mention...I think Kylekatarn is from Portugal too ![]()
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
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....




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?
You are right, Mathsy!

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.
![]()
Yes, very much British ![]()
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 ![]()
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?
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.
Playing
justlookingforthemoment
MathsIsFun
Mathsyperson
Zach
insomnia
Ganesh may be added to the list ![]()
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.