There are 10,000 crew members standing around the edge of a ship. The Captain goes around and pushes every other crew member off starting with the first person. Who is the last person to get pushed off the ship.
Which number person survives?
Its isn't the captain...
Any ideas...if you know explain how you found the answer?
2007-11-02 12:28:02 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
if you know the answer i will be glad to award you triple points.
2007-11-02 12:28:57 · update #1
s = 2y + 1
where y = n - 2^x and x is max while y >= 0
y = 10000 - 2^13
= 10000 - 8192
= 1808
s = 2*1808 + 1
= 3617
2007-11-04 19:12:08 · answer #1 · answered by Mugen is Strong 7 · 1⤊ 0⤋
Cycle 1: everyone whose number is 0 mod 2 gets pushed off, and the last one pushed is 10000, so cycle 2 begins with 1. There are 5000 left
Cycle 2: Pushed off are 3, 7, 11... those equal to 3 mod 4. Last one is 9999, so cycle 3 starts at 1 also
Cycle 3: pushed off are 5, 13, ... equal 5 mod 8. Last one is 9995, so cycle 4 starts at 1 also
Continue this way for about 13 cycles and you will find the answer.
2007-11-02 12:57:26 · answer #2 · answered by sofarsogood 5 · 0⤊ 0⤋
This is isomorphic to this problem I answered a few weeks ago:
http://answers.yahoo.com/question/index;_ylt=ApDBxLztCOcMcF2sn2vm_DLty6IX;_ylv=3?qid=20071008015354AAdj4ql&show=7#profile-info-AA11505348
If you scroll down to my answer, (which somehow didn't get selected as best despite the fact that it had a clear mathematical derivation and the BA did not), you see that the person who survives a game with n people is 1 + 2(n-2^k), where 2^k is the largest power of 2 less than n. Here, we have n=10000, so the largest power of 2 less than 10000 is 2^13 = 8192. So the survivor is person 1+2(10000-8192) = 1809.
2007-11-03 11:14:18 · answer #3 · answered by Pascal 7 · 0⤊ 0⤋
Just an idea. The captain is #10001, so he,s gotta go
too. This leaves # 10000 to bring the ship home
2007-11-02 12:40:31 · answer #4 · answered by Grampedo 7 · 0⤊ 0⤋
at the instant mine has been going back and forth between sixteen-17%...yet i've got self assurance this is on sluggish downward trend simply by fact some months in the past it grew to become into around 19-20%...by the tip of the year i'm hoping to be at one million-2%. whilst it is going to a damaging form, which would be my clue to bypass on..
2016-10-03 05:19:25 · answer #5 · answered by riobe 4 · 0⤊ 0⤋
4999 or 5000, the captain pushes every OTHER person off...
2007-11-02 12:41:40 · answer #6 · answered by Thallasa35 2 · 0⤊ 0⤋
wouldn't it be the 10,000 person?
im not a genius but i think it is.
2007-11-02 12:36:06 · answer #7 · answered by Courtneyyyy(: 1 · 0⤊ 0⤋