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Seven - with and without (Posted on 2013-08-09) Difficulty: 2 of 5
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

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts 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
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