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07 Jul 2020, 03:04
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At a wedding reception, twelve guests sat together at a round table. At the end of the meal, before they left, each guest at the table kissed all of the other guests goodbye. What was the total number of kisses?
A. 24
B. 55
C. 66
D. 78
E. 132
A. 24
B. 55
C. 66
D. 78
E. 132
yashikaaggarwal
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Last visit: 10 Aug 2026
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07 Jul 2020, 04:37
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Total no. Of kisses = Sum of N-1 number of guests = sum of 11 positive number of guests
Sum = 11(11+1)/2
Sum = 11*12/2
Sum = 11*6
Sum = 66
Therefore total 66 kisses were been done at the table.
Alternatively,
Let the guests be 1,2,3,..........12
1 will kiss every other guest except himself.
(1,2)
(1,3),(2,3)
(1,4),(2,4),(3,4)
(1,5),(2,5),(3,5),(4,5)
(1,6),(2,6),(3,6)......,(5,6)
(1,7),(2,7),(3,7).......,(6,7)
(1,8),(2,8),(3,8).........,(7,8)
(1,9),(2,9),(3,9)..........,(8,9)
(1,10),(2,10),(3,10)........,(9,10)
(1,11),(2,11),(3,11).........,(10,11)
(1,12),(2,12),(3,12)..........,(11,12)
Total no. Of kisses = 11+10+9+8+7+6+5+4+3+2+1 = 66
Posted from my mobile device
Sum = 11(11+1)/2
Sum = 11*12/2
Sum = 11*6
Sum = 66
Therefore total 66 kisses were been done at the table.
Alternatively,
Let the guests be 1,2,3,..........12
1 will kiss every other guest except himself.
(1,2)
(1,3),(2,3)
(1,4),(2,4),(3,4)
(1,5),(2,5),(3,5),(4,5)
(1,6),(2,6),(3,6)......,(5,6)
(1,7),(2,7),(3,7).......,(6,7)
(1,8),(2,8),(3,8).........,(7,8)
(1,9),(2,9),(3,9)..........,(8,9)
(1,10),(2,10),(3,10)........,(9,10)
(1,11),(2,11),(3,11).........,(10,11)
(1,12),(2,12),(3,12)..........,(11,12)
Total no. Of kisses = 11+10+9+8+7+6+5+4+3+2+1 = 66
Posted from my mobile device
07 Jul 2020, 05:57
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The round table is irrelevant. Every (unordered) pair of people creates one kiss, and we can pick 12C2 = (12)(11)/2! = 66 pairs of people, so that's the answer.
