In a class of nine students, each students sends valentine cards to three others. Determine whether it is possible that each student receives cards from the same three students to whom he or she sent cards.
Answers
Given : In a class of nine students, each students sends valentine cards to three others
To find : Determine whether it is possible that each student receives cards from the same three students to whom he or she sent cards.
Solution:
number of students = 9
Each students Send card to three others
Hence total Card Distributed = 9 * 3 = 27
it is not possible that each student receives cards from the same three students to whom he or she sent cards.
Similar transaction need to be in pair to happen this
like a sent b => b sent a
Hence total transaction need to be in even number
but transactions are in odd number hence not possible
if it have been 8 students then it would have been possible
sender receiver
1 2 3 4
2 1 3 4
3 1 2 4
4 1 2 3
5 6 7 8
6 5 7 8
7 5 6 8
8 5 6 7
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