ATERNITY OUTING The fraternity brothers at some other fratenities. They planned
ID: 3148507 • Letter: A
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ATERNITY OUTING The fraternity brothers at some other fratenities. They planned to attend a pie-eating contest together. There were 5 members of Phi Phi Pho Phum, 4 members of Eta Pi, 3 members of Nu Kappa, 2 members of Beta Zeta Theta, and 1 member of Tau Rho. They all met in front of the library to drive over to the contest. Unfortunately, they only had one vehicle: an old, beat-up Volkswagen "Bug." They figured it would hold 6 people plus the driver John Vernon, dean of the fraternity council. The giant Phi Phi Pho Phum members were exceptions to this formula. Each of them took up as much room in the car as 2 members of any other fratemity. To further complicate matters, many of the fraternities were fiercely competitive and would play practical jokes on some of the others, even if outnumbered. The competitors are as follows: the Tau Rho member would be quite eager to play a trick on anyone else from any of the other fratemities. Any of the Nu Kappa members would gladly play tricks on any of the Eta Pi members. Any of the Phi Phi Pho Phum members would gladly make fun of any of the Beta Zeta Theta members. No tricks would be played in the car while Dean Vernon was present, and no tricks would be played once all 15 members were together at the pie-eating contest. How did Dean Vernon arrange the transportation in the least number of trips, so that no member played a trick on anyone else? Phi Phi Pho Phum had arranged an outing withExplanation / Answer
Conditions to be fulfilled at the destinations.
Tricks are played by the party members only at the venue.
Therefore at the venue the following combinations should not be present to avoid playing tricks among them.
Thus the mixing of the following combinations should be avoided at destinations till all members are assembled along with the Dean
Groups to be avoided.
No. of members of the group are as follows.
Tau Rho 1
Beta Zeta Theta 2
Nu Kappa 3
Eta Phi 4
Phi Phi Pho Phum 5
Total members 15
But since Phi Phi Pho Phum occupies two seats we have to consider them as 10 for transportation.
This 20 to be ferried with a capacity to go in one trip 6. Thus (20/4) , four trips are mandatory. But this is not the minimum as ferrying in a unorganised manner may create playing jokes at the venue.
Therefore the goat-tiger-grass formula problem should be extended to solve this problem.
A minimum of 4 Trips from the Library to the Venue is sufficient to ferry all the members.
Details are as follows.
Three Phi Phi Pho Phum are ferried.
No. of members at Destination is equal to 3.
One Phi Phi Pho Phum and Four Eta Phi members are ferried.
No. of members at destination now equals 8
One Phi Phi Pho Phum Travelled
No. of members at destination equals 9
Three Nu Kappa and Two Beta Zeta Theta and one Tau Rho Travels
Number of members at destination 15
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