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

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

Hey you guys are pretty smart

Ideas are funny little things, they won't work unless you do.

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**katie****Member**- Registered: 2005-07-13
- Posts: 5

hi

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

Hello Katie

Ideas are funny little things, they won't work unless you do.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 23,353

Jenilia wrote:

Hey you guys are pretty smart

Thanks, Jenilia. Visit the 'Games and Puzzles' topic regulalry. I shall post mathematical problems and their solutions which could be of some help to you, for the Olympiad.:)

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

Thanks Ganesh

Ideas are funny little things, they won't work unless you do.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 23,353

Jenilia, we shall prepare you for the Olympiad;

I shall start with my first lesson,

do you know how recurring decimals are converted into fractions?

Lets assume x=0.1414141414....................

100 x = 14.14141414.....................

Deducting equation (2) from (1),

99x = 14

x = 14/99

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

Ganesh, to tell the truth I don't understand you

Ideas are funny little things, they won't work unless you do.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 23,353

There are two types of decimals:- Terminating and recurring.

A number like 12.5 or 1.25 or 3.75 is a terminating decimal.

On the other hand, sometimes, you have numbers like 0.33333333333333.................,

0.166666666666.....................,

1.6666666666666 etc which are called recurring decimals.

For example, 1'/2 or 1/8 is a terminating decimal.

1/3, 5/6 etc are recurring decimals.

I was talking about how recurring decimals are convereted into rational numbers (that is, fractions).

If that is clear, look at the following illustration.

How do we convert 2.166666666666.............. into a rational number?

Let x = 2.16666666666666666............

10 x = 21.66666666666666666.......... ----------(I)

100x = 216.6666666666666666......... ----------(II)

Subtracting (I) from (II),

90x = 195,

x = 195/90 or 13/6.

Now, have I made myself clear?

*Last edited by ganesh (2005-07-19 22:28:42)*

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**insomnia****Real Member**- Registered: 2005-03-23
- Posts: 944

The UKMT is basically a survey to see how people think in relation to maths. The tests are quite hard with Beginner (first 2 or 3 years of secondary school), Intermidate (last years of 2nd school) and higher is probably A-levels or University.

The test aims to find out how people think, etc.

You get 25 q's or something. The first 10 you get 5 points for each q, 11-25 you get 6 points but you lose 1 point in q's 11-20 and 2 points in q's 21-25. Can't remember exactly, but I did it every year. It was for the highest maths sets in every year.

It is very hard

Friends are angels who lift our feet when our own wings have trouble remembering how to fly

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,664

Maybe we could find some sample questions

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

I posted some links on that earlier.

mathsyperson wrote:

If you want to try some of the questions, there are some samples here or try the most recent junior, intermediate or senior past papers.

Why did the vector cross the road?

It wanted to be normal.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,664

Well, perhaps we could take one of those questions, and try reasoning it out, so that Jenilia and everyone else can learn techniques.

For example, samples from your first link:

Junior:

"The sum of seven, single-digit positive whole numbers is 17. Six of these numbers are equal, so what is the other number?"

Intermediate:

"Alice's room is furnished with three-legged stools and four-legged chairs. There are 17 legs in all (excluding Alice's!). How many three-legged stools are there?"

Senior:

"The cards in a set of 36 are numbered 1 to 36. The cards are shuffled and four cards are dealt. What are the chances of them being dealt in descending order?"

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

Maths is fun, can you explain the answer for the seniors question.

Ideas are funny little things, they won't work unless you do.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,664

I guess it doesn't matter how big the deck of cards is, so long as we know they are unique numbers.

So, it is really as easy as thinking "I choose the numbers 1 to 4 in random order, what are the chances of them being perfectly 4321?"

Do you want to try to figure THAT one out? (Hint: how many combinations are possible, and how many match what you are after?)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**anyarules****Member**- Registered: 2005-07-24
- Posts: 29

[be nice] Anyone from Australia?? we just recently did a olympiad test and i got 3/5. how saad. it's about this ant walking around this cube.

*Last edited by MathsIsFun (2005-07-26 00:13:53)*

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

Hey, maybe you can try next time. Anyway I just participated in the best in school competition. Out of 360 students I came in the second.

Ideas are funny little things, they won't work unless you do.

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

I got a question to ask? Nora can paint 1/6 of a house in 1 day. Meera can paint the whole house 2 days faster. If both of them paint the house together, how long will they take.

The answer is 2 3/4 days. I figured out the answer in school which is correct. But when I came home I forgot the answer. Now I am dieing to know the answer.

Ideas are funny little things, they won't work unless you do.

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**ganesh****Administrator**- Registered: 2005-06-28
- Posts: 23,353

Nora can paint 1/6 of a house in 1 day.

Therfore, she takes 6 days to paint the house.

Meera can paint the whole house 2 days faster.

So, she can paint the house in 4 days.

In one day, Meera can paint 1/4 of the house.

If both of them paint the house together, in one day,

they can paint (1/6+1/4) of th house. That is,

10/24 or 5/12. Therefore, the whole house can be painted

by them in 12/5 days, that is 2 2/5 days.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

Thanks for teaching me Ganesh.

Ideas are funny little things, they won't work unless you do.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,664

I was impressed by how well you did in your in school competition. Jenilia.

Please visit more, try some of the puzzles ganesh sets, and ask any quesitons you want.

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**wcy****Member**- Registered: 2005-08-04
- Posts: 117

yeah 2nd is school is really good

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

You call that good? I only got 16/30 you know, for the standard.

Ideas are funny little things, they won't work unless you do.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,664

Depends on the questions ...

Glad you are back again, Jenilia!

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**Jenilia****Member**- Registered: 2005-07-09
- Posts: 64

Of cause I am back

Ideas are funny little things, they won't work unless you do.

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