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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

I recently received 100 "out of the world maths question" from somebody, I complete them but stuck with a few, so help will be great, also explanation on how you did it please.

Q1) A student wrote down the following sequence of numbers : the first number is 1, the second number is 2, and after that, each number is obtained by adding together all previous numbers. Determine the 12th number in the sequence.

A1) My answer is 1536, I did it bu writing it all on a piece of paper by adding them all up, there is a better way to do it right?

Q2) Adam has £2010 in his bank account. He donates £10 to charity every day. His first donation is on Monday. On what day will he donate his last £10?

A2) My answer is Monday, I did it by drawing it all up. I'm sure there is a better way to do it? Please show me how.

Q3) A circle and a square overlap such that the overlapping area is 50% of the area of the circle, and is 25% of the area of the square. Find the ratio of the area of the square outside the circle to the area of the whole figure.

A3) I have no idea about his one, please show me how you did it.

Q4) Find the number of different pairs of positive integers (a,b) for which

andA4) I do not understand please show me how you did it.

Q5) There positive integers a,b and c are given such that

Find the value of a,b and c.

A5) I do not understand at all.

Q6) Find the number of positive integers less than 500, which is not divisible by 5 or 7.

A6) I know how to do this all on a big piece of paper, but there is a easier way? Please show me how.

Q7) Find the smallest positive integers n such that every digit of n is either 0 or 7, and n is divisible by 15.

A7) Again, I could do that on a big piece of paper, but please show me a easier way to do it.

Q8) Let n and k be two positive integers such that k is less than n. It is known that (1+2+3+4+...+n) + k = 101. Find k.

A8) I do not know how to do this.

Q9)Find the last digit of :

A9) This one got to do with mod?

That's all, thanks everyone. p.s I need help with modifying it... Like the way I do it with a few more answers, I might post it later.

EDIT*** Can someone show me the worked method?

*Last edited by David (2014-06-15 23:34:43)*

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

Hi chooipian

For Q1, you can just write out all the numbers.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Oh.. Okay, but for the rest?

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

Hm, it seems that's how you did it. Didn't see that there were your answers beneath the questions. I'll look at Q2.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Hi,

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,037

Hi chooipian

*Last edited by anonimnystefy (2014-06-15 02:52:14)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

These questions seem familiar...

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

You saw it before?

btw, How to find the area of a circle when an equilateral triangle with sides 2 units is inscribed in the circle? It's not Heron's Formula?

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Have you copied the all questions correctly?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Yes.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

These are from the Malaysian National Olympiad! I remember doing these!

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

I told you it's out of this world...

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

ShivamS wrote:

These are from the Malaysian National Olympiad! I remember doing these!

I have no idea, I got it from a Senior... That's where it's from -_- When did you did that? Mind teaching me?

*Last edited by David (2014-06-15 03:02:23)*

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

aops.com has a lot of past contest and Olympiad papers available online so I searched it there.

I don't really remember when I did this, probably a few years back (I recognized a problem from it).

*Last edited by ShivamS (2014-06-15 03:03:06)*

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Looked at them, but I have a lot that are not in it!...

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Opps sorry bobbym, I edited question 4.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

For now, I think I'll go to rest first. I have school tomorrow morning, I will get back to this when school is over tomorrow.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Hi;

I knew you had a mistake there if you wanted an answer less than infinity.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,648

Good night.

I'll work on them now.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

Have a good night.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

Good night, good evening or good morning to you all too.

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606

You are supposed to say "Good night Mrs. Calabash wherever you are."

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**** Always satisfy the Prime Directive of getting the right answer above all else.**

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,592

Hi chooipian,

Thanks for those puzzles...I've enjoyed doing them.

These are the ones I could do...with explanations (though not always fully or step-by-step). Q4 and Q5 have got me beat for now.

*Last edited by phrontister (2014-06-16 10:26:14)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,135

bobbym wrote:

You are supposed to say "Good night Mrs. Calabash wherever you are."

Who is Mrs. Calabash? Good Morning Mrs. Calabash wherever you are. And Good Morning to everyone else too!

*Last edited by David (2014-06-16 00:06:11)*

Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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