Technothlon 2016 hauts

As the leader of his island Tintin has decided to take matters into his own hands and rebel against the king.

THE ISLAND

• Question 1 Before leaving, he wants to test whether his friend Captain Haddock is wise enough, so he places three boxes A.B,C contain initially 0, 0, 27 balls respectively. He tells that he wants equality among the boxes, and at every $i^{th}$ move you make, you must transfer exactly $i$ balls from one box to another. And you cannot transfer balls between A and B. How many minimum steps are required (if possible) to get into equal number of balls in each box?

A). 7 B). 9 C).8 D) Not possible.

• Question 2 Walking along, Tintin overheard the two island gate guards, Thomson and Thompson chatting among themselves.

Thomson: He told us that we have consecutive letters on our papers.

Thompson: Yeah he told me too.

Thomson: I don't know what your letter is.

Thompson: Neither do I know your letter.

Thomson: Now I know.

Tintin listened this conversation and wondered what the two letters could be. When he was about to leave island Thomson stopped him and told him to say the password, which were the two letters. Maximum of how many attempts does Tintin need to make to have the correct pair of letters, and thus pass successfully?

A). 1 B). 2 C). 4 D). More than 4

THE SCIENTIST'S HELP

• Question 3 After leaving his island, Tintin seeked the help of tge great scientist Dr Calculus who stayed in his research island When he landed on the island, he notices a map of 25 labs, aligned in a 5x5 pattern, of which a few labs were burned (Coloured in figure). Only 15 labs from #1 to #15 are not burnt.

He noticed the map, but realised that the numbers were missing from it. Instead, an instruction read "The distance from lab #1 to lab #2 will be less than the from lab #2 to lab #3. which is less than the distance from lab #3 to lab#4, and so on". Also, only the intact labs were numbered. Find out the value of a+ b(where a and b are the lab numbers). Note that the Distance is calculated from the centre of one to the centre of another.

A). 10 B). 12 C). 14 D). 16

After coming out of his town, Tintin goes to Al Capone's island to gather more followers to assist him in his revolution.

AL CAPONE'S ISLAND

• Question 4 Al capone and his n-1 friends are sitting in a circular fashion when Tintin meets them(sitting of n people). Each of them owns coin. First person passes 1 coin to the Person on his left side. The second person in turn passes 2 coins to the person siting on the left Third person passes 1 coin to the left, 4th passes 2 coin to his left and so on, So each person receiving coin from the right has to pass 2 coins to the left Similarly, a person receiving 2 coins from the right has to pass I coin to the left.

If at any point of time, a person runs out of coin he is thrown out of the game. The game will terminate if at the end only 1 person is with coins in his possession. There might be walues of n where the game may not terminate e g 3 persons left with 4 4 4 coins respectively For how many different values of n from 4 to 100 does the game terminate?

(a) 16 (b) 7 (c) 46 (d) 10

• Question 5:

Capone loved balances. He took Tintin to his famous room of Balance where there was present a huge complex balance as shown in the fig The marks on the stick are at 1 metre distance each and the white small circles represent the paint around which the stick is hinged. There are 12 identical looking weights which weigh 1kg, 2kg, 3kg upto 12kg. He asked Tintin to identify the weight of each of the weights given that the stem is balanced Tintin identified 9 of them correctly except the encircled ones, can you help him in telling the sum of the weights of the encircled ones? For balancing the total system all the sticks that hold the weights need io be balanced themselves. For each of the stick being balanced the following condition need to be satisfied

A)17 B)18 C) 19 D) 20

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