/sci/ - Science & Math » Thread #11501192

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Anonymous Wed 25 Mar 19:32:08 2020 No.11501192 View Reply Original Report

Quoted By:

i solved this but it took me like 10 minutes of trial and error. is there a systematic way to solve this problem?

Anonymous

Anonymous Wed 25 Mar 2020 23:36:33 No.11501775 Report

Quoted By:

bump

Anonymous

Anonymous Wed 25 Mar 2020 23:42:58 No.11501792 Report

Quoted By: >>11501864 >>11503662

first, note that inversions dont count, since the ratio is the same. so 1:2 is 2:1

second, since its 3 equivalent ratios, the denominator cant be greater than 3. because, since you need 3 of them, the minimum multiplier for denominator is 3 (4*3=12). so your denomintaros can be 1, 2, or 3. 1 and 3 dont work by checking, so you have two options left for 2, and only one works,so thers ur answer

1/2
3/6
4/8

Anonymous

Anonymous Thu 26 Mar 2020 00:03:40 No.11501864 Report

Quoted By: >>11501869

>>11501792
you misread the question, you need to use all numbers 1-9 and you need to have the digits aligned with the underlines in the picture

Anonymous

Anonymous Thu 26 Mar 2020 00:04:43 No.11501869 Report

Quoted By: >>11502470 >>11503495

>>11501864
anyhow the actual answer i found is
6:3, 18:9, 54:27. how would you get this systematically?

Anonymous

Anonymous Thu 26 Mar 2020 03:06:01 No.11502316 Report

Quoted By:

bump. i found this on an elementary school teacher’s twitter and i figured someone on /sci/ would be able to derive a method (or at least solve it before i posted the solution but i already needed to post it to prove a retard wrong)

Anonymous

Anonymous Thu 26 Mar 2020 04:39:36 No.11502470 Report

Quoted By:

>>11501869
5 pretty much confines you to a pretty small set of numbers. 0 isn't available, so for any even factor, 5 must appear in the first digit of of one of the 2-digit numbers. For 1:2 it must be the first digit of the last ratio, meaning that the other two digit number must be 26-29. So 5,2 are taken. 1 is taken for a factor of two since it must be in the first digit of the second ratio. The second digit of the second ratio must then be 4, 6, or 8 to be divisible by 2. The first pair can then be 3:6 or 4:8. Now it's pretty trivial to search the space. Anything above 1:4 isn't possible because 1 would be needed in the first and last ratio. 1:4 can be reasoned through like 1:2. 1:3 can as well, since 5 similarly has to go in the first digit of the last ratio since any number ending in 5 multiplied by 3 will also end in 5, so it needs to be 17, 51 18, 54 or 19, 57 in the last ratio.

There's not really a formula for it, but you can go pretty quickly taking a Sudoku like approach and simply stating what must be true for it to work.

Anonymous

Anonymous Thu 26 Mar 2020 14:43:28 No.11503495 Report

Quoted By:

>>11501869
dont forget 6/3=14/7=58/29, fren
I) second ratio leads to >1
II) first ratio leads to <4
III) second ratio must be 12/4,12/6, 18/6, 18/9, 21/7, 24/8 or 27/9
Test for 24/8 and 27/9 -> doesnt work -> second ratio must include "1" -> only possible ratio is 2
III) First ratio is either 4/2, 6/3, 8/4 -> the rest is sudoku

Anonymous

Anonymous Thu 26 Mar 2020 16:04:09 No.11503662 Report

Quoted By:

>>11501792
1:2 is not equivalent to 2:1
by definition

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