All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Seven - with and without (Posted on 2013-08-09)
Let us divide a set of all n-digit numbers into two subsets:
N7- whose members contain at least one 7 and Nw - whose members are 7-free ,e.g. for n=2 there are 18 members in N7: 17,27,37,... 70, 71,72, …79, and there are 72 members in Nw.
Let us denote those quantities by q7 and qw: q7(2)=18 and qw(2)=72.

Evaluate q7(n) and qw(n) for the following values of n:

n=5
n=42
n=100

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: solution | Comment 5 of 6 |
(In reply to solution by Charlie)

An afterthought:

My D2  question would be more interesting and challenging if instead of asking to apply the formula for certain values I would ask for which minimal n  f7 is larger than fw.

This idea was triggered by Ch's remark:
..."7-digit numbers are the first where there are more numbers with 7 than without."

 Posted by Ady TZIDON on 2013-08-09 17:44:56

 Search: Search body:
Forums (0)