Guys, some help...
Whats the best math formula to resolve this ?
(i came out with that one, pic related, but i'm not sure)
"All natural numbers bellow 1000000 i can form using only the 0~9 digits, without repeating them and not accepting only zero nor zeros to the left.
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bump!
>not accepting only zero nor zeros to the left
So 0, 00, 000, etc. don't count? 100, 386, count, but 0100, 00100, 00386 do not count?
yes, its the all the set W is all about.
wut ?
Okay, well, you need to have at least one non-zero digit. You can pick this in 9 ways (one for each digit 1 to 9). Since you want a number less than 1000000, you can have at most 5 digits.
Thus, you can pick the first digit in 9 ways: one for each digit from 1 to 9. The rest of the digits are chosen from the remaining 9 (0 to 9, excluding the one your first picked). Order matters, so you use permutations:
You can pick k digits in 9*P (9,k-1) ways, so just sum that from k = 0 to 5
...
Why did you write 9-(x-1) and not 10-x tho
...
Your solution's right. K is the amount of numbers you can make that don't have repeating digits and W is the amount of those numbers that start with a zero, which is a tenth. So K-W is the amount of non-repeating numbers that don't have 0's on the left.
...
hi
...
to keep the same ratio 1~6, 1 meaning one digit and 6 the maximum allowed digit (last number would be 999999, 6 digits).
But i guess there's no math formula other than summation of combinations. Well, thanks anyway.
1) This belongs to 2) I smell homework
3) It's a really simple task, statistics 101:
First we get all numbers with 6 digits:
The first digit has 9 possibilities (1-9), second number also 9 (0-9 minus the previous one) and so on - so it's "9 * 9 * 8 * 7 * 6 * 5" possibilities.
And so on.
No fuck off.
By the way, I get the same result as you:
(9 * 9 * 8 * 7 * 6 * 5)
+ (9 * 9 * 8 * 7 * 6)
+ (9 * 9 * 8 * 7)
+ (9 * 9 * 8)
+ (9 * 9)
+ 9
=
136,080
+ 27,216
+ 4,536
+ 648
+ 81
+ 9
=
168570
yes man, i did it, in case you didn't notice its answered, i'm just looking to improve my answer.
i can do some simplification as:
import math
f = math.factorial
r = 0
for i in range(1,7):
r+=(f(10)-f(9))/f(10-1)
print(r)
i mean:
for i in range(1,7):
r+=(f(10)-f(9))/f(10-i)
why isn't the answer 999999 for all numbers below 100000 that aren't 0?
can't repeat digits 0~9
its just 987654 the higher one
You can also write it like this:
9 * 9 * 8 * 7 * 6 * 5 ( 1 + 1/5 + 1/(6*5) + 1/(7*6*5) + 1/(8*7*6*5) + 1/(9*8*7*6*5) )
Then you can transform it into this:
9 * (9!/4!) * ( 1/(4!/4!) + 1/(5!/4!) + 1/(6!/4!) + 1/(7!/4!) + 1/(8!/4!) + 1/(9!/4!) )
Which is the same as:
9 * (9!/4!) * 4! * (1/4! + 1/5! + 1/6! + 1/7! + 1/8! + 1/9!)
And finally:
9 * 9! * (1/4! + 1/5! + 1/6! + 1/7! + 1/8! + 1/9!)
I doubt it gets any shorter than this.