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

Home > Just Math
So close, but no closer... (Posted on 2014-12-04) Difficulty: 3 of 5

Determine the value of the smallest positive integer N such that N1/N contains precisely one zero immediately following the decimal point.

Too easy?

How about seven zeroes, then?

See The Solution Submitted by broll    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer assisted solution | Comment 1 of 5
A graphing calculator table shows

 N     N^(1/N)                                                                     
38  1.100457444033732                                                             
39  1.098491064028148                                                             

so part 1's answer is 39.

Part 2:

After narrowing it down somewhat via calculator, the following code, actually at the first iteration of i, finds N = 190660033.957375 produces 1.0000001.

 n1 = 190660000#: v1 = n1 ^ (1 / n1)
 n2 = 190670000#: v2 = n2 ^ (1 / n2)
 For i = 1 To 50
   frac = (1.0000001 - v1) / (v2 - v1)
   n1 = n1 + (n2 - n1) * frac
   v1 = n1 ^ (1 / n1)
   Text1.Text = Text1.Text & n1 & Str(v1) & crlf
   DoEvents
 Next
 
To narrow it down further, I used UBASIC under DOSBox, with more precision than what is shown below: 

Immediate mode of UBASIC says

N = 190660033 produces 1.0000001000000006368
N = 190660034 produces 1.0000001000000001398
N = 190660035 produces 1.0000000999999996428

Part 2: answer is 190,660,035

Edited on December 4, 2014, 2:22 pm
  Posted by Charlie on 2014-12-04 14:21:37

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (2)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information