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 2019-11-06, 15:14 #1 enzocreti   Mar 2018 10248 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 2019-11-06 at 15:20
 2019-11-06, 15:30 #2 Uncwilly 6809 > 6502     """"""""""""""""""" Aug 2003 101ร103 Posts 1053810 Posts 6210 is 1111102
 2019-11-06, 16:55 #3 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 144728 Posts N = 2 210 = 1.1111.....2
2019-11-06, 17:25   #4
VBCurtis

"Curtis"
Feb 2005
Riverside, CA

14A716 Posts

Quote:
 Originally Posted by retina N = 2 210 = 1.1111.....2
That contains more than 5 ones.

2019-11-06, 17:56   #5
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

193A16 Posts

Quote:
 Originally Posted by VBCurtis That contains more than 5 ones.
Yes. The criterion is that is contains five ones. And it does. It also contains some more ones. It didn't say five ones and only five ones.

 2019-11-06, 18:12 #6 VBCurtis     "Curtis" Feb 2005 Riverside, CA 17×311 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.
2019-11-06, 18:15   #7
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

2·3,229 Posts

Quote:
 Originally Posted by VBCurtis 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.
But you might find me pedantic.

 2019-11-06, 18:25 #8 M344587487     "Composite as Heck" Oct 2017 19×47 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
2019-11-06, 18:32   #9
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

2×3,229 Posts

Quote:
 Originally Posted by M344587487 -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".
2 and -0 have the same "number of digits when written in base 10". But 2 has fewer characters than -0.

But a true pedant might interpret "smallest" to be numerical value. And if we are allowed to twist the definition boolean arithmetic with infinity: "-(โ AND (โ 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.

2019-11-06, 20:28   #10
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

11,317 Posts

Quote:
 Originally Posted by VBCurtis 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.
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.

2019-11-06, 21:52   #11
Dr Sardonicus

Feb 2017
Nowhere

169A16 Posts

Quote:
 Originally Posted by retina N = 2 210 = 1.1111.....2
The question specified "converted in base 2."

Please explain the algorithm by which you convert 210 into base two, so as to get 1.111... rather than 10.

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