Puzzle : The Logical Team Work

Thirty fans hire a bus to attend a football game. On the way to the stadium, they realize that exactly half of them are fans of one team and the other half are fans of the other team. With still some way to go before reaching the stadium, the bus develops mechanical problems and the driver announces to his passengers that the only way to continue the journey is for half of them to get out and walk. There is a huge fight that doesn't stop until the driver speaks to them again and suggests a way of selecting the passengers who are to get off the bus.

"All of you," he said, "get into a big circle. When you are ready, beginning at this spot, I'll count nine people clockwise. The ninth person leaves the circle and continues on foot. Then I'll count another nine starting from where I stopped, and the ninth person leaves the circle and continues on foot. And so on until fifteen people have left the circle."

Suppose that you are one of the fans. How should you arrange all the other fans of your team so that none of them will have to leave?

This should be your ARRANGEMENT! 

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.    

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.