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**Sum of no.**

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**juan****Guest**

(1) The sum of all no. that can be formed by using the digits

(2) Total no. of positive Integer solution of

(3) Total no. of positive Integer solution of

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

For (1): Must all the digits be used in making one number?

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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,797

Q1. There are 7 digits. Pretend they are all different, a,b,c,d,e,f,g say.

Find all the possibilities:

a, ab, abc, .......fg, g

Now allow for the repeats by dividing (eg if all 4s then divide by 4!)

Might be easier to count by taking all the 4s; then only three 4s then only two etc.

Q2. No number can be over 10 or under 1.

So 10 + 1 + 1

9 + 2 + 1

9 + 1 + 2

etc. It's not so bad to continue like this, is it?

That should show you a generating technique which will make Q3 easy.

Bob

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,891

bob bundy wrote:

Q1. There are 7 digits. Pretend they are all different, a,b,c,d,e,f,g say.

Find all the possibilities:

a, ab, abc, .......fg, g

Now allow for the repeats by dividing (eg if all 4s then divide by 4!)

Might be easier to count by taking all the 4s; then only three 4s then only two etc.

Q2. No number can be over 10 or under 1.

So 10 + 1 + 1

9 + 2 + 1

9 + 1 + 2etc. It's not so bad to continue like this, is it?

That should show you a generating technique which will make Q3 easy.

Bob

We don't need the number of those kind of nos in tthe first problem. And in the second problem, the numbers an also take on a negative value...

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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 92,964

Hi juan;

For 1)

I am getting 399999960. I am assuming you want to use all seven numbers to form a seven digit number.

For 2) I am getting 578.

For 3) I am getting 4672.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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