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

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

#11

Post by Cogito »

pavel_lishin wrote: post #7
jlarocco wrote: post #5

The 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.

An easy way to try this is to consider any that start with 1+2+3.

You can create a second version by replacing this with 1×2×3.

For example,

    10914 = 1 × 2 × 3 × (4^5 + 6 + 789)
    10914 = (1 + 2 + 3) × (4^5 + 6 + 789)

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

#12

Post by happimess »

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…

It's not clear from your formatting, but the line was

  1 = 1 ^ 23456789
I thought it was really cool that this pattern is used elsewhere to collapse any prefix into 1, e.g.

  9 = (1 ^ 2345678) * 9

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

#13

Post by [deleted] »

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…

[deleted]

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

#14

Post by monk_e_boy »

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…

I didn't read the article... but why 1 to 9? Is it because we have 10 fingers and 10 symbols that represent numbers? We're this numbers chosen for another reason?

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

#15

Post by javajosh »

happimess wrote: post #12
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…

It's not clear from your formatting, but the line was 1 = 1 ^ 23456789 I thought it was really cool that this pattern is used elsewhere to collapse any prefix into 1, e.g. 9 = (1 ^ 2345678) * 9

Thanks. Copy/pasted from PDF and it got lost. Fixed.

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

#16

Post by andrepd »

monk_e_boy wrote: post #14
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…

I didn't read the article... but why 1 to 9? Is it because we have 10 fingers and 10 symbols that represent numbers? We're this numbers chosen for another reason?

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

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

#17

Post by monochromatic »

andrepd wrote: post #16
monk_e_boy wrote: post #14

Earlier quoted context omitted.

I didn't read the article... but why 1 to 9? Is it because we have 10 fingers and 10 symbols that represent numbers? We're this numbers chosen for another reason?

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.

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

#19

Post by aaron695 »

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.

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

#20

Post by lanna »

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.
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