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Solution : The Logical Team Work


What was the puzzle?

Let's number the first person from where the drive starts counting first as 1. So there are 30 people standing in circle and we have numbered them in clockwise direction. 

Remember, driver starts counting another nine starting from where he stopped to give a moment for 9th person to leave.

Let's divide the elimination process into rounds.

In every round of driver's counting few fans will be eliminated as below.

Round 1 - 

Counting starts clockwise from 1, 10 and 19,

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30

Fans standing at 9, 18 and 27 are asked to leave. 

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30

Total eliminations after Round 1 = 3.

Round 2 -

Counting started from 28, 7 and 17,

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30

Those who are standing at 6, 16 and 26 have to start walking. 

1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30

Total eliminations after Round 2 = 6. 

Round 3 - 

Counting starts with 28, after 9 counts it starts with 8 & it resets when 19 is eliminated,

1, 2, 3, 4, 5, 7, 8, 10, 11, 12, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 28, 29, 30

People standing at 7, 19 and 30 need to leave.

1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 15, 17, 20, 21, 22, 23, 24, 25, 28, 29

Total eliminations after Round 3 = 9.  

Round 4 - 

Counting starts with 1 and after 9 counts it starts with 13, 

1, 2, 3, 4, 5, 8, 10, 11, 12, 13, 14, 15, 17, 20, 21, 22, 23, 24, 25, 28, 29 

Here, persons at 12 and 24 should leave. 

1, 2, 3, 4, 5, 8, 10, 11, 13, 14, 15, 17, 20, 21, 22, 23, 25, 28, 29 

Total eliminations after Round 4 = 11.  

Round 5 - 

Now, Counting starts with 25 and after 9 counts it starts with 10, 

1, 2, 3, 4, 5, 8, 10, 11, 13, 14, 15, 17, 20, 21, 22, 23, 25, 28, 29

That is persons at 8 and 22 need to start walking. 

1, 2, 3, 4, 5, 10, 11, 13, 14, 15, 17, 20, 21, 23, 25, 28, 29 

Total eliminations after Round 5 = 13.  

Round 6 -  

Counting starts with 23 and after 9 counts it starts with 10, 

1, 2, 3, 4, 5, 10, 11, 13, 14, 15, 17, 20, 21, 23, 25, 28, 29  

Obviously, fans standing at 5 and 23 have to leave. 

1, 2, 3, 4, 10, 11, 13, 14, 15, 17, 20, 21, 25, 28, 29

Total eliminations after Round 6 = .  15

That's it! Now, driver can easily drive those remaining 15 fans to the football stadium.    



The Arrangement of Your Teammates


CONCLUSION : 

You should arrange your teammates to the below positions in order to save them from elimination process - 

 1, 2, 3, 4, 10, 11, 13, 14, 15, 17, 20, 21, 25, 28, 29.
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