From Technothlon 2014 Paper
Midhul and seven of his friends go to Accoland, a famous amusement park in Guwahati.
Against all odds they decide to play bumper cars. The available cars are of various colours blue, green, purple & red, and luckily there are exactly two of each colour. Hence, they decide to form teams of two, with each team occupying the cars of one particular colour. Midhul & Saichran are team-mates and so are Mayank & Kenil. The game proceeds and each member tries to bump as many opponent team members as possible. Team-mates obviously do not bump each other(not even by accident).
If player A bumps player B, then player B will immediately take revenge and bump player A.The game comes to an end, and everyone enjoys themselves thoroughly. Midhul bumped Mayank just before the game ended. He is curious to know the status of the other players. He goes around and asks everyone (other than himself) how many distinct players they have bumped. Surprisingly, each of them gives a different answer (they have very good memory, and are completely honest) Answer the following questions:
Question 1 How many distinct players did Saicharan bump?
Question 2 How many distinct players did Midhul bump?
If answer of Question 1 is 1 and that of Question 2 is 4 then your answer should be 14 .
The answer is 33.
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1 solution
Each one of his 7 friends gave hin a different answer. The maximun of different people anyone could hit it was 6. So the other friends hit 0,1,2,3,4 and 5 (we will use these names to call them). The guy who bumped 6 people can only be in the team with the 0, because he hits everyone else. Now the 5 can only team up with the 1, because 5 didnt hit 0, 5 or 1(who only bumped 6). 4 made pair with 2(who bumped 5 and 6). And 3 made pair with Midhul (who didnt hit 0, 1, 2 or , his teammate, 3. So Midhul bumped 4, 5 and 6, 3 different people and his partner also bumped 3 different people. The answer will be 33.