Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

p and c

how many times the digit

is written while writing the numbers from

to

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: p and c

hi juantheron

I think the method on

http://www.mathisfunforum.com/viewtopic.php?id=16950

post number 6 will work here.

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

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: p and c

Hi;

I think you mean 1 000 000 000.

Digits from 0 to 9:

Start with the vector,

that represents the number of [1,2,3,4,5,6,7,8,9]'s used to make the digits from 0 to 9.

Digits from 10 to 99:

That says you need 19 sevens in the numbers from 10 to 99.

Digits from 100 to 999:

Digits from 1000 to 9999:

Digits from 10 000 to 99 999:

Digits from 100 000 to 999 999:

Digits from 1 000 000 to 9 999 999:

Digits from 10 000 000 to 99 999 999:

Digits from 100 000 000 to 999 999 999:

No we just add them all up.

That is all the numbers from 0 to 999 999 999. So there are 900 000 000 sevens in the numbers from 0 to 1 000 000 000.

You should see the pattern now that makes this computation easy for all numbers except 0, which is a special case that requires a little more work.

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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.

careless25

Real Member

Registered: 2008-07-24

Posts: 560

Re: p and c

Arent there 20 7s in 1-99??

7, 17, 27, 37, 47, 57, 67, 77, 87, 97, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: p and c

Yes, I said from 10 to 99, I am still filling in the post.

---

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.