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

You are not logged in.

- Topics: Active | Unanswered

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

What are the circumstances? What is he trying to do? Why can he not get his CAS working? Please give details...

**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.**

Offline

1. He was sitting in a computer center with many computers.

2. He was trying to get the coefficient of x^99 in (x+1)(x+2)(x+3)...(x+100). But he has already asked that.

3. There was no CAS in the computer center.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

He could have tried Alpha?!

**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.**

Offline

Alpha was not working because JS was disabled over there and when he enabled it, malwares and Ads started eating him up.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Then he must solve it by other means.

**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.**

Offline

Yes, he did.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,913

If you are going to compete over the speed of your code in producing an answer, you should, in fairness, add on the time it took to type the code. I did the problem in my head in about 5 seconds. I submit that is quicker.

And the OP didn't ask for quick code; he asked for confirmation that his answer was correct. And it wasn't posted in the coder's corner.

I further submit that the human brain is always superior, as coding can not be done without it.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

Please teach me how to do this in 5 seconds?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,913

hi Agnishom,

I cannot guarantee that everyone will take just 5 seconds. This is about how long it took me.

To get x^99, you need to multiply one x from each of 99 brackets, and a number from the other bracket. This diagram shows how you might do one such multiplication, where the i th bracket is the one which supplies the number.

which will give i.x^99

There are exactly one hundred choices for this special bracket, so the coefficient is found by adding all the possible values of i :1 + 2 + 3 + ... + i + ... + 100.

You can either use the formula for this or do :

(1+100) + (2 + 99) + (3 + 98) + ........ + (50 + 51) = 101 x 50 = 5050.

Bob

*Last edited by bob bundy (2014-09-24 01:52:50)*

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

Hi bob;

If you're have some time to spare please sign up at brilliant.org and look at this solution.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

Never mind.

We have done it the same way. It took much more than 5 seconds though.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 7,913

hi Agnishom,

Combinatorics is a new field to me so I looked it up on Wiki. They give binary trees as an example so how about this:

The diagram shows the first three lines of a binary tree. The i th line has branches that show 'x' if you go left and 'i' if you go right. You negotiate the tree by starting at the top and deciding whether to go left (x) or right (1). Then you have to decide which way to go at the second decision point, left (x) or right (2). And so on. The full tree has 100 lines so the last decisions are between left (x) and right (100).

Let's say you score zero for each x, and the number otherwise. You go down the tree choosing left 99 times and right just once There are 100 different ways you can do this. What is the total score if you add up all these individual scores.

It's now the same as my brackets; 1 + 2 + 3 + ... + i + ... + 100

Any use ?

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Offline

Look this up the wiki? How?

https://brilliant.org/community-problem … lOy0moidHR

There is a button saying 'Reveal 2 solutions'. Please click it

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Why not do it using the methods of EM?

**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.**

Offline

How do I do that?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

The human mind is a pattern spotter. That is really all it is good for. It is so good at it, it can spot a pattern when one does not even exist.

How do I do that?

Hmmm you surely must have heard of top - down design?! Or do you need some help with that?

**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.**

Offline

I see.

The problem has been solved anyway.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Yes, it has been solved but do you know what I mean?

**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.**

Offline

Yes, you want me to do it with two terms, then three terms, then four and then make a pattern of it.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

That is almost correct, make you sure you multiply intelligently.

**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.**

Offline

Intelligent multiplication?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

Offline

**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,407

Only multiplying up to the terms you need.

**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.**

Offline