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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Hi, could you verify if my answer is correct ? I DON'T WANT THE ANSWER, I just want my work to be verified:

Several digits "8" are written and some "+" signs are inserted to get the sum 1000. Figure out how it is done (For example, if we try 88+88+8+88+8, we fail because we get only 280 insted of 1000.)

My answer(It may be long) :

1-First, the number 1000 is composed of 125 digits "8", because :

2-This limits us to 3 principal number in our sequence of numbers, which will help us build 1000.

8: He is composed of only one digit 8.

88: He is composed of 11 digit 8.

888: He is composed of 111 digit 8.

3-Now, there exists different ways to build the number 1000(Depending of the composition of your sequence of numbers.)

4-If your sequence of numbers is composed of the number 888(Which can only go one time in your sequence.), this results in this :

a) 125-111=14 numbers "8" left.

You could now continue your sequence by 88 because:

14-11=3 numbers "8" left. Then, finish off your sequence by 3 digits "8", because :

3-3=0 digits "8" left.

b) Or, you could have had 888 in your sequence, which would give :

125-111=14 chiffres '8' left.

And then, complete the sequence by 14 digits 8.

14-14=0 digits "8" left.

5)If your sequence contains one or many times the number 88, it should give :

a) Maximum of 88 composed in the number 1000: 11 times

11*88=968

digits "8" in total

125-121=4 digits '8'* left

To obtain 1000, we must add 4 times the digit 8

4-4=0 digits "8" left.

We can then conclude that there exists 11 ways possible to have 1000 with a sequence of numbers which contains at maximum 11 times the number 88 and at minimum 1 time the number 88.

Each time you will remove a "88" in your sequence, it will be needed to be replaced by 11 times the digit 8 so we can keep the answer equalling 1000.

Ex: 88+88+88+88+88+88+88+88+88+88+88+8+8+8+8=1000

Now, we will remove a "88"

88+88+88+88+88+88+88+88+88+88+**8+8+8+8+8+8+8+8+8+8+8**+8+8+8=8=1000

6- Finally, the last way of obtaining 1000 consists to write 125 times the number 8.

8+8+8+8...125 times

In total, you will have 14 ways of having one thousand.

Do you think I've figured out how it's done ? Or not ? No answers, just suggestions about what I wrote. Thank you!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

Hi;

This is somewhat different than your other questions. Verification of your reasoning can be supplied by a simple technique. It will take time though.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Ah... But you read my text??? And what do you mean by your technique ?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

We can then conclude that there exists 11 ways possible to have 1000 with a sequence of numbers which contains at maximum 11 times the number 88 and at minimum 1 time the number 88.

Correct!

In total, you will have 14 ways of having one thousand.

Correct!

I can find no hole in your reasoning and you have the correct answer.

The simple technique involves the number of solutions to the Diophantine equation.

Given that 0 ≤ a,b,c ∈ N

Your answer is proved using generating functions.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Ah, I don't know about that equation. (I'm still learning)

Thank you again ! I had the answer in my book, but I didn't want to see it,(and still haven't) just wanted it to be checked by someone who had experience ! Thanks !

*Last edited by Al-Allo (2013-07-07 13:01:22)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

Very interesting work, you did well.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

I'm happy to hear these comments ! I'm even happier to know that a person like you exists to help me in needs !

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

I am glad to help but I really only exist to eat and watch Cameron Diaz movies.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**Al-Allo****Member**- Registered: 2012-08-23
- Posts: 294

Well, I guess each person will give a different meaning to his existence

Anyway, I'll go now. Bye Bye !

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,237

Hi;

Okay and see you later.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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Athipthi wrote:

19. The OP stated they have registered the phone in their name (I didnt know you could do that when its a contract phone taken out in someone elses name?) so I doubt the original owner could get the phone barred once the details have been transferred over?

correct!!!!

'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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

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