Since 10x is by definition x1+0 this is indeed very obvious. This also implies that it is possible to write any number in such a way that it ends in a zero. Now, the more interesting thing to think about is, given an integer n, what is the maximum number of zeros you can make it end with by picking an appropriate basis?
The easier way to phrase is is "the highest power in the prime factorisation." For example: 28=7⋅22, so the highest power is 2. Indeed, 28 in binary is 11100. The highest number of ending zeros also always occurs in a prime number basis. Although that number does not need to be unique to one basis. For example 36=33⋅22, so it ends in two zeros in both basis two (3610=1001002) and basis three (3610=11003).
Hahah, you've gotta refine the question a bit. The answer as posed is infinite as you can have arbitrarily small fractional bases. For a integral base you can give another cheat answer. Base 1 with a symbol of 0 such that 51 = 00000. An integral > 1 base is an interesting and ostensibly tricky one though!
Not always. You're making unstated assumptions. There are many varied number systems other than those with which people are generally familiar. Here's one example. https://en.wikipedia.org/wiki/Bijective_numeration
Jesse Howell on Twitter: "@notch @kkearns Ah... I get it now. I like Base 10 (binary) and base 10 (hexidecimal), but I use base 10 (decimal) most often."
https://archive.is/tPA4t : Jesse Howell on Twitter: "@notch @kkearns Ah... I get it now. I like Base 10 (binary) and base 10 (hexidecimal), but I use base 10 (decimal) most often."
Jesse Howell on Twitter:"@notch @kkearns Ah... I get it now. I like Base 10 (binary) and base 10 (hexidecimal), but I use base 10 (decimal) most often."
No shit, the values of the digits, from left to right, are multiples of xn, xn-1, xn-2, . . . , x2, x1, x0. To answer your question, anyone who has taken a single computer science class has thought about it.
17 comments
8 u/0x5f3759df 07 Jul 2016 06:59
Since 10x is by definition x1+0 this is indeed very obvious. This also implies that it is possible to write any number in such a way that it ends in a zero. Now, the more interesting thing to think about is, given an integer n, what is the maximum number of zeros you can make it end with by picking an appropriate basis?
2 u/tame 07 Jul 2016 08:23
Ooh, nice puzzle. I think the number of zeroes is equal to logk x for the smallest integer k which produces an integer logarithm.
There's probably a nicer way to phrase that.
3 u/0x5f3759df 07 Jul 2016 16:24
The easier way to phrase is is "the highest power in the prime factorisation." For example: 28=7⋅22, so the highest power is 2. Indeed, 28 in binary is 11100. The highest number of ending zeros also always occurs in a prime number basis. Although that number does not need to be unique to one basis. For example 36=33⋅22, so it ends in two zeros in both basis two (3610=1001002) and basis three (3610=11003).
0 u/flat_hedgehog 21 Jul 2016 17:45
Nice! Thank you for a puzzle on my day off.
1 u/rwbj [OP] 07 Jul 2016 08:34
Hahah, you've gotta refine the question a bit. The answer as posed is infinite as you can have arbitrarily small fractional bases. For a integral base you can give another cheat answer. Base 1 with a symbol of 0 such that 51 = 00000. An integral > 1 base is an interesting and ostensibly tricky one though!
1 u/0x5f3759df 07 Jul 2016 16:03
Well, yes. Integers only, and integer bases only.
2 u/varialus 07 Jul 2016 09:14
Not always. You're making unstated assumptions. There are many varied number systems other than those with which people are generally familiar. Here's one example. https://en.wikipedia.org/wiki/Bijective_numeration
2 u/tame 07 Jul 2016 12:42
Spot the pure maths junkie. :P
2 u/derram 07 Jul 2016 11:11
https://archive.is/tPA4t :
This has been an automated message.
1 u/rwbj [OP] 07 Jul 2016 11:13
Looks good!
1 u/derram 07 Jul 2016 07:10
https://archive.is/tPA4t :
Jesse Howell on Twitter: "@notch @kkearns Ah... I get it now. I like Base 10 (binary) and base 10 (hexidecimal), but I use base 10 (decimal) most often."This has been an automated message.
3 u/rwbj [OP] 07 Jul 2016 08:28
Nice bot. Might be better to use the standard quote system with '>' instead of the code block since there's no word wrap in code blocks.
0 u/derram 07 Jul 2016 08:34
Can't use quotes on a line that already contains text, >like this.
3 u/rwbj [OP] 07 Jul 2016 08:42
I was just thinking something like this:
https://archive.is/tPA4t :
This has been an automated message.
2 u/derram 07 Jul 2016 09:31
Best I could do would be to toss the text onto a new line as a quote, the bot is pulling that text from the title since it mainly targets articles.
0 u/Tommstein 14 Jul 2016 06:15
No shit, the values of the digits, from left to right, are multiples of xn, xn-1, xn-2, . . . , x2, x1, x0. To answer your question, anyone who has taken a single computer science class has thought about it.
0 u/flat_hedgehog 21 Jul 2016 17:43
Yes, but it's a realisation the first time.