Struck Down
Math brain teasers require computations to solve.
One hundred people stand in a row
Each has a rank from go to whoa
Every fifth one is struck from the line
This is repeated time after time
'til at last there is only five left in line
What is the original rank of the one on the end this time?
HintThey line up numbered from 1 to 100 and every fifth person leaves the line. This continues till only 5 remain.
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Answer
Initially the rank of the last person is 100. Every fifth person is struck out of the line. Since 100 is divisible by 5 this person leaves. Thus the last 2 ranking persons are now the (original) 99th and 98th and there are 80 people left. Every fifth person now leaves, including the last one originally ranked 99 so the last person is now the original ranked 98th. 80/5 is 16 so 16 have left with 64 remaining. Now, 12 leave (64/5) down to 52. Then 10 leave (52/5) with 42 remaining. 8 leave with 34 remaining; 6 leave with 28 remaining; 5 leave with 23 remaining...19...16...13..11...9,8,7,6,5. To this point none of the remaining queues have been evenly divisible by 5 so the last person has always stayed. The person originally ranked 98th is still here!
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Comments
krishnan
Sep 27, 2003
 A good fun puzzle. Enjoyed that! 
heyevpos
Feb 16, 2004
 Thank you, very enjoyable. I spent 2 minutes figuring whoa minus 2 (9 as the numerical rank. Then, about 20 minutes trying to figure an algorithm to decipher what the name of the rank should be since the ranks were given as go to whoa. Could not find one. Lots of fun. 
javaguru
Feb 17, 2009
 Easy and fun. 
stil
Apr 18, 2009
 Mind you this is just a quibble, but every line has two ends, so while 98 is the last to hold the "whoa" end 1 is still at "go" end. 
stil
Apr 18, 2009
 "at last there is nly five"??? Amn't "are" more gooder grammer? 
Jimbo
Apr 19, 2009
 "Go" means start and "Whoa" means stop so although there are two ends of a line it implies that there is a starting end and a finishing end.
As for 'there is only five'  hey it's a poem so cut me some slack with the poetic licence! 
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