This is way more numerology than math, and I don't see any deep results coming out of this. Was this just a fun side project for the author?
Not everything that's written as an article is serious :)
Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
41–50 of 61 posts
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#42Seems related to this recent Numberphile video which does a similar thing for e and pi:
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#43Would 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.
Huh, he does 98 as 98=1×23+45+6+7+8+9.
Or do you mean that 23 and 45 are cheating, because they are two digit numbers? I think they rules are quite well explained and followed.
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#44Interesting fact: every integer can be written with three 2's.
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#45Interesting fact: every integer can be written with three 2's.
n + (2 - 2) / 2 ?
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#46Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#47I 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.
Reminds me so much of competitive programming
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#48Interesting fact: every integer can be written with three 2's.
-log_2 log_2 sqrt(...(sqrt(2))...) {with n copies of sqrt} = -log_2 (2^-n log_2 2) = -log_2 (2^-n) = -(-n) = n.
I would say that you need only one 2 if you replace log_2 by lg, so we should make lg taught in high schools... wink
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#49Earlier quoted context omitted.
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.
I assume 111112 is unrepresentable as well?
To me, the pattern of unrepresentable numbers (like the pattern of primes) would also be an "interesting" result.
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#50So, who is going to find the increasing solution for 10958?