Math Is Fun Forum

juan

Banned

Sum of no.

(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: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Sum of no.

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

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“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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,648

Re: Sum of no.

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

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Sum of no.

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

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...

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“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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Sum of no.

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.

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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.