Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

arxiv.org

Post reply on HN
Print view View original

21–30 of 61 posts

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#21

Post by Retra »

javajosh wrote: post #10

It wasn't clear why this was interesting from the title. But here's an example: 0 = 12 + 34 − 56 − 7 + 8 + 9. 1 = 1^23456789. 2 = 123+4−56−78+9. 3 = 123 − 45 − 6 − 78 + 9. And then in decreasing order 0 = 98−7−6−54−32+1. 1 = 98−76−54+32+1. 2 = 9+87−65+4−32−1. 3 = 98−76−5+4+3−21. That this is possible at all is counter-intuitive to me, and hence fascinating. Even more fascinating is that he does not have a solution fo…

There's not a lot interesting about "facts about numbers" when you place such a low upper bound on your achievements. If he'd only done this up to 100, he'd never have had trouble finding a solution for 10958. But why 11111? Why not 111111111111?

To me this is just as interesting as any other arbitrary list of permutations of symbols.

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#22

Post by aaron695 »

lanna wrote: post #20
aaron695 wrote: post #19

Would be more interested in the script than the list and how long it took to run. And if this is the best so far? Seems surprising given it's a popular kids game. It's not really maths IMO since I think using 98 is cheating for instance, it's really (9 X 10 + 8), 10 not being allowed. So kids are not learning real maths, more arithmetic.

There is no script, he did it mostly by hand.

I would have thought that to be the fun bit!

I think there was at least one script for some of the numbers, this I would have thought the most interesting, optimisation of the script and for all numbers and proving some numbers have no solutions([edit] possibly very hard) -

"The author is thankful to xxxx in finding some difficult representations using computerized script."

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#23

Post by adtac »

I just wrote a script to do this in, like, 5 minutes :) And the whole thing runs in 7 seconds on my machine.

https://github.com/adtac/123456789/blob/master/output

Admittedly, it doesn't have every number. I suspect it's because I haven't included bracketed expressions.

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#24

Post by adtac »

aaron695 wrote: post #19

Would be more interested in the script than the list and how long it took to run. And if this is the best so far? Seems surprising given it's a popular kids game. It's not really maths IMO since I think using 98 is cheating for instance, it's really (9 X 10 + 8), 10 not being allowed. So kids are not learning real maths, more arithmetic.

I just wrote a tiny script that does this: https://github.com/adtac/123456789/blob/master/main.py

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#25

Post by 7373737373 »

adtac wrote: post #23

I just wrote a script to do this in, like, 5 minutes :) And the whole thing runs in 7 seconds on my machine. https://github.com/adtac/123456789/blob/master/output Admittedly, it doesn't have every number. I suspect it's because I haven't included bracketed expressions.

What happens if you allow for 0?

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#26

Post by saghm »

monochromatic wrote: post #17
andrepd wrote: post #16

Earlier quoted context omitted.

There are 10 one-digit numbers in decimal. 0 is excluded because of obvious reasons, leaving numbers 1 through 9.

In other words, yes, we use decimal because we have ten fingers.

Is that actually why base 10 became the norm? I've never really learned why exactly decimal was chosen, and I'd be interested in learning about what historical evidence there is for its origin.

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#27

Post by throwaway982749 »

saghm wrote: post #26
monochromatic wrote: post #17

Earlier quoted context omitted.

In other words, yes, we use decimal because we have ten fingers.

Is that actually why base 10 became the norm? I've never really learned why exactly decimal was chosen, and I'd be interested in learning about what historical evidence there is for its origin.

Well... there's evidence right there in the English language.

    dig·it [ˈdijit]

    NOUN
    1) any of the numerals from 0 to 9, especially when forming part of a number.
    2) a finger (including the thumb) or toe.

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#28

Post by nullc »

saghm wrote: post #26
monochromatic wrote: post #17

Earlier quoted context omitted.

In other words, yes, we use decimal because we have ten fingers.

Is that actually why base 10 became the norm? I've never really learned why exactly decimal was chosen, and I'd be interested in learning about what historical evidence there is for its origin.

It's often claimed, but I'm not aware of any strong evidence for it.

In particular, since our hands can show "10" the natural base this would imply is base _11_ and not 10.

Another argument I've heard presented is that since 10 is divisible by 2 and 5 this simplifies many common calculations. There were groups in the past advocating use of other bases (in particular 12 but also 16).

The mayan's number system is base 20 (though the digits are are drawn out of sub digits in base-5).

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#29

Post by [deleted] »

saghm wrote: post #26
monochromatic wrote: post #17

Earlier quoted context omitted.

In other words, yes, we use decimal because we have ten fingers.

Is that actually why base 10 became the norm? I've never really learned why exactly decimal was chosen, and I'd be interested in learning about what historical evidence there is for its origin.

[deleted]

Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)

#30

Post by metaphor »

adtac wrote: post #23

I just wrote a script to do this in, like, 5 minutes :) And the whole thing runs in 7 seconds on my machine. https://github.com/adtac/123456789/blob/master/output Admittedly, it doesn't have every number. I suspect it's because I haven't included bracketed expressions.

  3 = 123+4+5-6*7^89
First verifiable instance of error?

Did a little fishing for overflow candidates with the following regex:

  [1-9]{3,}\^[1-9]{3,}
...caught 58 results between 266 and 10940:

  266 = 123^456-78-9
  ...
  10940 = 12345^6789
My kung fu isn't Python so I don't know how types are handled. That eval() function sure smells suicidal for anything remotely serious though.
Post reply on HN