Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
1–10 of 61 posts
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#2Why did this paper need four revisions?
Edit: the revisions have different ranges of numbers, but they go up and down. Odd.
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#3[deleted]
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#4Why is this even a thing?
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#5The abstract and introduction don't explain this very well.
My understanding is that the author wrote the digits 1 through 9 in ascending order, and then inserted parenthesis, addition, subtraction, multiplication, division and exponentiation operators between them where appropriate to get every number from 0 to 11111.
And then he did the same thing using the digits 9 through 1 in descending order and did the same thing.
He was able to find a solution for every number except 10958 with 1-9 in ascending order.
EDIT:
The paper also doesn't explain much about how or why they did this. At first glance I don't think it would be too difficult to come up with a branch and bound algorithm to search through all the solutions.
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#6At my office we lost a lot of time because someone put up a challenge to represent all the numbers 0-99 with algebriac expressions containing exactly four digits '4'. The use of powers and radicals was allowed.
I myself solved several numbers before exhausting the tricks I could think of, and reverted to brute force/search with Polish/prefix notation, then realizing how massive the search space was for even just a few operators. Adding parentheses ordering further explodes the search space.
Finally, while this kind of concrete and explicit expression is "toy math", it is related to Godel Sentences and lexigraphic ordering of proofs used through much of the establishment of logic, the foundations of proof systems, and computer science.
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#7The abstract and introduction don't explain this very well. My understanding is that the author wrote the digits 1 through 9 in ascending order, and then inserted parenthesis, addition, subtraction, multiplication, division and exponentiation operators between them where appropriate to get every number from 0 to 11111. And then he did the same thing using the digits 9 through 1 in descending order and did the same th…
I wonder if any numbers have multiple solutions.
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#8The abstract and introduction don't explain this very well. My understanding is that the author wrote the digits 1 through 9 in ascending order, and then inserted parenthesis, addition, subtraction, multiplication, division and exponentiation operators between them where appropriate to get every number from 0 to 11111. And then he did the same thing using the digits 9 through 1 in descending order and did the same th…
I wonder if any numbers have multiple solutions.
I am nearly certain many do.
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#9Maybe something neat to bring up as a "drinking game"...at my next Math Symposium
Pick at random 3 digit number and try to express using the digits 1 thru 9...loser has to drink
Re: Numbers 0 to 11111 in terms of Increasing and Decreasing Orders of 1 to 9 (2014)
#10It 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.
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.