Struck DownMath 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.
AnswerInitially 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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