But we do shake hands with enemies!
Rajdeep
,
Parth
,
Panshul
and Archit are students studying in Grade 9. They are sitting in a room with 2015 students studying in Grade 8.
We know that Rajdeep doesn't shake hands with enemies. Out of the 2015 8th Graders, 500 are Rajdeep's enemies. Rajdeep can shake hands with everybody else in the room. Archit shakes hands only with Rajdeep's enemies. Parth and Panshul are best friends and they shake hands only with each other.
If all other 2015 people can shake hands with any other person in the room, how many handshakes took place?
Details and Assumptions :
1) If A can shake hands with B, but B can't shake hands with A, they will not shake hands.
2) If A and B can shake hands with each other they will surely shake hands.
3) 2 people can't shake hands with each other multiple times.
Image Source: keenetrial.com
The answer is 2031121.
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Let, A are number of handshakes made by 2015 Grade 8 students:
A = ( 2 2 0 1 5 ) = 2 0 2 9 1 0 5
Let, B are the number of handshakes made by Rajdeep with 1515 Grade 8 students:
B = ( 1 1 5 1 5 ) = 1 5 1 5
Let, C are the number of handshakes made by Archit with 500 Rajdeep's enemies
C = ( 1 5 0 0 ) = 5 0 0
Let, D are the number of handshakes made by Parth and Panshul
D = ( 2 2 ) = 1
The total number of handshakes made are:
T o t a l = A + B + C + D
T o t a l = 2 0 2 9 1 0 5 + 1 5 1 5 + 5 0 0 + 1
T o t a l = 2 0 3 1 1 2 1