Latest TCS Aptitude Question SOLUTION: 49. 48 people {a1, a2,...... a48) meet and shake hands in a circular fashion. In other words, there are totally 48 handshakes involving the pairs, {a1, a2}, {a2, a3}, ...{a47, a48}

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49. 48 people {a1, a2,...... a48) meet and shake hands in a circular fashion. In other words, there are totally 48 handshakes involving the pairs, {a1, a2}, {a2, a3}, ...{a47, a48}, {a48, a1}. Then the size of the smallest set of people such that the rest have shaken hands with at least one person in the set is
O 16
O 24
O 17
O 15

Asked In TCS juhe rawat (10 years ago)

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Debabrata Roy Chowdhury  (10 years ago)

Ans: 16 (Quite popular and common question!)
Thought process:
It is said to form the smallest subset, look here:
a2 shakes hand with a1 & a3.
a4 shakes hand with a3 & a5.
a6 shakes hand with a5 & a7.
- - - - - - - - - - - - - -

- - - - - - - - - - - - - -
a48 shakes hand with a47 & a1 and likewise in circular manner.

So the smallest possible selection would be to select from the set of these 3 elements, {a1,a2,a3}..and so on..
This was just the analysis, now the trick!

Trick:
N/3 where N=Number of people in the meeting(and not the number of handshakes!)
So, 48/3 = 16

Is this solution Helpfull? Yes (24) | No (1)  

Kundan Kumar  (10 years ago)

16 ( a1,a2,a3) If we take in set of three persons. Since it is cyclic order.
Therefore, at one person has handshaked with the other person.
48//3= 16
Ans is 16

Is this solution Helpfull? Yes (3) | No (1)  

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