Junior : Enigmathic

ENIGMATHIC

As you reach Iraq, you see 49 people fighting among themselves to split their prize money. Many don't want to divide it into 49 equal parts as they worked harder than the others. To resolve the issue, the Owl suggests a way: "If 50% or more people in the group agree on splitting equally, then they will split equally. If not, the person with the least contribution loses his claim, and is out of the

group. The voting continues till a solution is reached".(ex : Suppose there are 10 people left. If 5 or more agree to divide the prize money equally, each would get an equal share. If not, the 10th ranked person is out of the group, and voting continues with the 9 people left).

Question 10:

In short, among how many people should the prize money be divided equally if every person is self-centred and every time he/she votes, tries to get maximum bene fit?

After your suggestion, the people of Iraq pay you a little as a reward for your help. Later, on your way to a hotel you find some people debating on an issue. Help them resolve it and earn some more money in return for your favour.

Question 11:

The issue is:

The government of Iraq wants to issue ‘d’ denominations of coins (in whole numbers of dinars(Iraqi currency)) so that by using no more than 3 coins, citizens can pay any amount from 1 dinar to 36 dinar. Find the value of ‘d’ and all the ‘d’ denominations and give the sum of all these ‘d’ denominations?

(Ex: if d=3 and 3 denominations are {4,5,3}, answer= 4+5+3= 12.)

Question 12:

After resolving the issue, you stop at the hotel to take rest for the night. Unfortunately, the hotel is owned by Poseidon. Poseidon is Athena's greatest enemy. Poseidon, on knowing that you are coming from Parthenon(Temple of Athena), decides to make life awful for all of you. There are 32 rooms in the hotel and there are 32 identical looking keys. He gives them all and says that the second heaviest key is the one which opens your room. He also says that there is a balance (it compares two keys at a time) which can be used only N times ,where N is the minimum number of comparisons required to fi nd the second heaviest key. What is the value of N?

Question 13:

Next, just to make your life even more diffi cult, he says that while you are checking out of the hotel, you should pay him any amount(in integer value of dinars) exactly that he asks (the maximum that he can ask is 302 dinars). So, you decide to divide 302 dinars into ‘N’ diff erent pouches such that you can pay him any amount from 1 to 302 dinars by giving certain number of pouches. What is the minimum value of ‘N’?

[Note: The above 4 questions are 2-digit integer type i.e., the answer can be any integer from 00 to 99].