20191106, 15:14  #1 
Mar 2018
17×31 Posts 
which is the smallest even number...
which is the smallest even number N (in base 10) such that converted in base 2 contains five 1's?
I guess 94? Last fiddled with by enzocreti on 20191106 at 15:20 
20191106, 15:30  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101Γ103 Posts
2×3×37×43 Posts 
62_{10} is 111110_{2}

20191106, 16:55  #3 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{2}×5×307 Posts 
N = 2
2_{10} = 1.1111....._{2} 
20191106, 17:25  #4 
"Curtis"
Feb 2005
Riverside, CA
2×3^{2}×5×53 Posts 

20191106, 17:56  #5 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{2}·5·307 Posts 

20191106, 18:12  #6 
"Curtis"
Feb 2005
Riverside, CA
2·3^{2}·5·53 Posts 
It also didn't say "at least 5 ones".
If I asked for a recipe using 3 eggs, and you gave me a recipe using infinite eggs, I wouldn't find you very helpful. 
20191106, 18:15  #7 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{2}·5·307 Posts 

20191106, 18:25  #8 
"Composite as Heck"
Oct 2017
13×61 Posts 
If we're going for pedantry points then you missed negative numbers. Pick a representation of negative numbers in binary, pick a fixed or variable word representation, pick how you define smallest. Naturally you'd think a<b for smallest, but the base 10 specification allows for an interpretation as the least number of digits when written in base 10.
0 is 11111 in one's complement with a 5 bit word. It's the default winner of "least number of digits when written in base 10". 
20191106, 18:32  #9  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{2}×5×307 Posts 
Quote:
But a true pedant might interpret "smallest" to be numerical value. And if we are allowed to twist the definition boolean arithmetic with infinity: "(β AND (β XOR 1))" has an infinity of 1's with the last digit as 0. Now we just need to define AND and XOR when dealing with infinities. 

20191106, 20:28  #10 
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
3×3,557 Posts 
Reminds me of the programmer who, before he went shopping, was told by his wife: "Buy a loaf of bread and, if they have any eggs, get a dozen." He came back with 12 loaves of bread and no eggs.

20191106, 21:52  #11 
Feb 2017
Nowhere
10645_{8} Posts 

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