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wu :: forums    riddles    easy (Moderators: SMQ, Grimbal, Eigenray, william wu, Icarus, ThudnBlunder, towr)    Writing special fractions « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Writing special fractions  (Read 2654 times) pcbouhid Uberpuzzler     Gender: Posts: 647 Writing special fractions   « on: Dec 1st, 2005, 9:32am » Quote Modify 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. IP Logged Don´t follow me, I´m lost too. hasup Newbie     Posts: 8 Re: Writing special fractions   « Reply #1 on: Dec 9th, 2005, 7:11am » Quote Modify hidden: 2=13458/6729 3=17469/5823 4=15768/3942 5=13845/2769 6=17658/2943 IP Logged JohanC Senior Riddler     Posts: 460 Re: Writing special fractions   « Reply #2 on: Dec 9th, 2005, 8:03am » Quote Modify 10 isn't possible with these rules, and I don't see a way to make 11. Here are some higher numbers: hidden: 73548 / 6129 = 12 81549 / 6273 = 13 27384 / 1956 = 14 27945 / 1863 = 15 98352 / 6147 = 16 91426 / 5378 = 17 28674 / 1593 = 18 51984 / 2736 = 19 IP Logged fatball Senior Riddler Can anyone help me think outside the box please?     Gender: Posts: 315 Re: Writing special fractions   « Reply #3 on: Dec 9th, 2005, 11:34am » Quote Modify hidden: 7=16758/2394 8=25496/3187 9=57429/6381 IP Logged pcbouhid Uberpuzzler     Gender: Posts: 647 Re: Writing special fractions   « Reply #4 on: Dec 9th, 2005, 11:57am » Quote Modify Nice work, all of you, specially JC that got beyond the limits... and I must confess that I didn´t even try (to achieve 11, 12...) when I read about this problem. IP Logged Don´t follow me, I´m lost too. fatball Senior Riddler Can anyone help me think outside the box please?     Gender: Posts: 315 Re: Writing special fractions   « Reply #5 on: Dec 9th, 2005, 12:23pm » Quote Modify One thing we know for sure is that 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). IP Logged JohanC Senior Riddler     Posts: 460 Re: Writing special fractions   « Reply #6 on: Dec 11th, 2005, 1:25pm » Quote Modify Yes, fatball, very good observation! Keep on pushing the limits! IP Logged JocK Uberpuzzler     Gender: Posts: 877 Re: Writing special fractions   « Reply #7 on: Dec 11th, 2005, 1:43pm » Quote Modify hidden: 154638 / 7029  =  22 134067 / 5829  =  23 143208 / 5967  =  24 172350 / 6894  =  25 120978 / 4653  =  26 102546 / 3798  =  27 129780 / 4635  =  28 105792 / 3648  =  29   End so on for 32, 33...   36 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. « Last Edit: Dec 11th, 2005, 1:49pm by JocK » IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. pcbouhid Uberpuzzler     Gender: Posts: 647 Re: Writing special fractions   « Reply #8 on: Dec 11th, 2005, 2:48pm » Quote Modify Jock, 0 is not allowed in the original, but it´s a good idea to change it (digits from 0-9), and ask for how many expressions one can write.   IP Logged Don´t follow me, I´m lost too. JocK Uberpuzzler     Gender: Posts: 877 Re: Writing special fractions   « Reply #9 on: Dec 11th, 2005, 3:04pm » Quote Modify i c.... (sorry, typical error from my side: starting working on the problem without properly reading the question ...   )   25 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.   « Last Edit: Dec 11th, 2005, 3:06pm by JocK » IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. JocK Uberpuzzler     Gender: Posts: 877 Re: Writing special fractions   « Reply #10 on: Dec 11th, 2005, 3:31pm » Quote Modify 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!       IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Writing special fractions   « Reply #11 on: Dec 12th, 2005, 12:23am » Quote Modify 87654312/9 = 9739368 87654321/9 = 9739369 IP Logged JocK Uberpuzzler     Gender: Posts: 877 Re: Writing special fractions   « Reply #12 on: Dec 12th, 2005, 3:30am » Quote Modify 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 ...   )     IP Logged solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it. xy - y = x5 - y4 - y3 = 20; x>0, y>0. info terbaru Newbie blackaholic     Gender: Posts: 5 Re: Writing special fractions   « Reply #13 on: Dec 13th, 2013, 6:35am » Quote Modify this should be in hard section       IP Logged UgoLocal02 Newbie     Gender: Posts: 31 Re: Writing special fractions   « Reply #14 on: Jun 12th, 2014, 1:13am » Quote Modify 81549 / 6273 = 13 27384 / 1956 = 14 27945 / 1863 = 15 98352 / 6147 = 16 91426 / 5378 = 17 28674 / 1593 = 18 51984 / 2736 = 19 IP Logged Pages: 1  Reply Notify of replies Send Topic Print Forum Jump: ----------------------------- riddles -----------------------------=> easy   - medium   - hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »

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