mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Blogorrhea > enzocreti

Reply
 
Thread Tools
Old 2019-11-06, 15:14   #1
enzocreti
 
Mar 2018

523 Posts
Default 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
enzocreti is online now   Reply With Quote
Old 2019-11-06, 15:30   #2
Uncwilly
6809 > 6502
 
Uncwilly's Avatar
 
"""""""""""""""""""
Aug 2003
101Γ—103 Posts

37×233 Posts
Default

6210 is 1111102
Uncwilly is offline   Reply With Quote
Old 2019-11-06, 16:55   #3
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

166A16 Posts
Default

N = 2

210 = 1.1111.....2
retina is offline   Reply With Quote
Old 2019-11-06, 17:25   #4
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

10E416 Posts
Default

Quote:
Originally Posted by retina View Post
N = 2

210 = 1.1111.....2
That contains more than 5 ones.
VBCurtis is offline   Reply With Quote
Old 2019-11-06, 17:56   #5
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

2×19×151 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
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.
retina is offline   Reply With Quote
Old 2019-11-06, 18:12   #6
VBCurtis
 
VBCurtis's Avatar
 
"Curtis"
Feb 2005
Riverside, CA

22×23×47 Posts
Default

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.
VBCurtis is offline   Reply With Quote
Old 2019-11-06, 18:15   #7
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

2·19·151 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
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.
retina is offline   Reply With Quote
Old 2019-11-06, 18:25   #8
M344587487
 
M344587487's Avatar
 
"Composite as Heck"
Oct 2017

631 Posts
Default

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".
M344587487 is offline   Reply With Quote
Old 2019-11-06, 18:32   #9
retina
Undefined
 
retina's Avatar
 
"The unspeakable one"
Jun 2006
My evil lair

2·19·151 Posts
Default

Quote:
Originally Posted by M344587487 View Post
-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: "-(∞ AND (∞ 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.
retina is offline   Reply With Quote
Old 2019-11-06, 20:28   #10
xilman
Bamboozled!
 
xilman's Avatar
 
"π’‰Ίπ’ŒŒπ’‡·π’†·π’€­"
May 2003
Down not across

2×23×223 Posts
Default

Quote:
Originally Posted by VBCurtis View Post
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.
xilman is online now   Reply With Quote
Old 2019-11-06, 21:52   #11
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

23×3×5×29 Posts
Default

Quote:
Originally Posted by retina View Post
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.
Dr Sardonicus is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Smallest 10^179+c Brilliant Number (p90 * p90) 2147483647 Factoring 29 2020-09-25 03:28
Could a Distributed Computing approach help find the smallest Brier number? jasong Math 5 2007-05-29 13:30
smallest number used in a mathematical proof? ixfd64 Lounge 22 2006-02-01 17:06
Can you find the smallest number? Fusion_power Puzzles 8 2003-11-18 19:36
Smallest untested number? wirthi Math 10 2003-10-05 13:02

All times are UTC. The time now is 21:04.

Sun Sep 27 21:04:49 UTC 2020 up 17 days, 18:15, 0 users, load averages: 1.98, 1.60, 1.53

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2020, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.