|
||
|
Title: Writing special fractions Post by pcbouhid on Dec 1st, 2005, 9:32am Using all the digits 1-9 once, write a fraction that is equal to 2. Do the same to achieve 3, 4, 5, 6, 7, 8 and 9. |
||
|
Title: Re: Writing special fractions Post by hasup on Dec 9th, 2005, 7:11am [hideb] 2=13458/6729 3=17469/5823 4=15768/3942 5=13845/2769 6=17658/2943 [/hideb] |
||
|
Title: Re: Writing special fractions Post by JohanC on Dec 9th, 2005, 8:03am 10 isn't possible with these rules, and I don't see a way to make 11. Here are some higher numbers: [hideb]73548 / 6129 = 12 81549 / 6273 = 13 27384 / 1956 = 14 27945 / 1863 = 15 98352 / 6147 = 16 91426 / 5378 = 17 28674 / 1593 = 18 51984 / 2736 = 19[/hideb] |
||
|
Title: Re: Writing special fractions Post by fatball on Dec 9th, 2005, 11:34am [hideb]7=16758/2394 8=25496/3187 9=57429/6381[/hideb] |
||
|
Title: Re: Writing special fractions Post by pcbouhid on Dec 9th, 2005, 11:57am [hide]Nice work, all of you, specially JC that got beyond the limits... and I must confess that I didnīt even try (to achieve 11, 12...) when I read about this problem.[/hide] |
||
|
Title: Re: Writing special fractions Post by fatball on Dec 9th, 2005, 12:23pm One thing we know for sure is that [hide]it won't work for any numbers ending in 0 (not allowed to use) or 1 (always ending up in same digit, thus violating the rule)[/hide]. |
||
|
Title: Re: Writing special fractions Post by JohanC on Dec 11th, 2005, 1:25pm Yes, fatball, very good observation! Keep on pushing the limits! |
||
|
Title: Re: Writing special fractions Post by JocK on Dec 11th, 2005, 1:43pm [hideb] 154638 / 7029 = 22 134067 / 5829 = 23 143208 / 5967 = 24 172350 / 6894 = 25 120978 / 4653 = 26 102546 / 3798 = 27 129780 / 4635 = 28 105792 / 3648 = 29 [/hideb] End so on for 32, 33... [hide]36[/hide] seems to be the first number not ending in '0' or '1' that can not be written in the form of a pan-digit fraction. |
||
|
Title: Re: Writing special fractions Post by pcbouhid on Dec 11th, 2005, 2:48pm Jock, 0 is not allowed in the original, but itīs a good idea to change it (digits from 0-9), and ask for how many expressions one can write. :o |
||
|
Title: Re: Writing special fractions Post by JocK on Dec 11th, 2005, 3:04pm i c.... (sorry, typical error from my side: starting working on the problem without properly reading the question ... ::) ) [hide]25[/hide] is the smallest positive number not ending in "0" or "1" that can not be represented by a pan-digit fraction that uses the digits 1-9 all once. |
||
|
Title: Re: Writing special fractions Post by JocK on Dec 11th, 2005, 3:31pm The next challenge: What are the largest subsequent integers that can both be represented in a fraction that uses the digits 1-9 each once? E.g. The pair (23, 24) does the job: 23 = 36294 / 1578 24 = 39528 / 1647 but it is certainly not the largest such pair! |
||
|
Title: Re: Writing special fractions Post by Grimbal on Dec 12th, 2005, 12:23am 87654312/9 = 9739368 87654321/9 = 9739369 |
||
|
Title: Re: Writing special fractions Post by JocK on Dec 12th, 2005, 3:30am I was hoping for a long race leading to ever larger pairs... Well done! (I think we may safely assume this pair to be the largest possible ... :) ) |
||
|
Title: Re: Writing special fractions Post by info terbaru on Dec 13th, 2013, 6:35am this should be in hard section ;D ??? ??? ??? |
||
|
Title: Re: Writing special fractions Post by UgoLocal02 on Jun 12th, 2014, 1:13am 81549 / 6273 = 13 27384 / 1956 = 14 27945 / 1863 = 15 98352 / 6147 = 16 91426 / 5378 = 17 28674 / 1593 = 18 51984 / 2736 = 19 |
||
|
Powered by YaBB 1 Gold - SP 1.4! Forum software copyright Đ 2000-2004 Yet another Bulletin Board |