|
||
|
Title: Tricky Sequence Post by navdeep1771 on May 15th, 2018, 1:03am Find the 1000th Term of the Sequence:- 1,3,5,7,9,11,13,15,17,19,31,33,35,37,39,51.....and so on. Note:- 1. Yes, there is "31" after "19" 2. It's a completely logical problem with a logical solution. |
||
|
Title: Re: Tricky Sequence Post by Grimbal on May 15th, 2018, 5:07am If there were a 7 then it would be all numbers with only odd digits. |
||
|
Title: Re: Tricky Sequence Post by navdeep1771 on May 15th, 2018, 8:18am Sorry @Grimbal for that mistake. I was in little hurry when I posted this question. Well, I modified it and you can try it now again. |
||
|
Title: Re: Tricky Sequence Post by Grimbal on May 16th, 2018, 5:19am That's a tough one. Maybe [hide]all integers with only odd digits[/hide]? |
||
|
Title: Re: Tricky Sequence Post by towr on May 16th, 2018, 1:14pm Well, in that case, the 1000th one would be [hide]13779[/hide] [hide]The easy way to find it is just run a script. The clever way to find it is to notice it's basically the integers in base five, but encoded with odd digits instead of consecutive digits. (1+1)/2 * 5 4 + (3+1)/2 * 5 3 + (7+1)/2 * 5 2 + (7+1)/2 * 5 1 + (9+1)/2 * 5 0 = 1000 [/hide] |
||
|
Title: Re: Tricky Sequence Post by Grimbal on May 17th, 2018, 5:36am Err... It seems that after reaching the first stumbling block, I didn't even read the end of the question. [hide]There are 5 1-digit, 25 2-digit, 125 3-digit and 625 4-digit numbers. A total of 780. 781st number is 11111. To get the 1000th, convert 1000-781 to base 5 and replace 01234 by 13579. 1000-781 = 219. In base 5 it is 01334 Replacing digits gives 13779[/hide] Towr is actually cheating. 1000 in base 5 is 13000. His so-called base 5 uses digits 1-5 and not 0-4. Which is actually cleverer than what I did. - But it is cheating. - Is it? But it works. - Yeah... it is the Kobayashi Maru all over again. |
||
|
Title: Re: Tricky Sequence Post by towr on May 17th, 2018, 10:12am Well, as I said (or at least suggested), I first found the answer just by running a simple loop over all numbers and counting the ones with only odd digits. The other way I found to get the answer is to convert to base 5, replace all 0s with 5s by borrowing from the preceding digit, and then double every digit and subtract 1. [hide] 100010 -> 130005 -> 124455+ -> 137795odd 62510 -> 100005 -> 44455+ -> 77795odd 78010 -> 111105 -> 55555+ -> 99995odd [/hide] |
||
|
Title: Re: Tricky Sequence Post by navdeep1771 on May 17th, 2018, 11:45am Well done guys! [hide] 13779 is the correct answer. [/hide] So you both (grimbal and towr) are correct and towr is really very clever. Well, I solved this problem with the same way as of grimbal. But yeah towr's approach is hard to get clicked. |
||
|
Powered by YaBB 1 Gold - SP 1.4! Forum software copyright © 2000-2004 Yet another Bulletin Board |