Tricky Trivia Question?

Question

The french ambassador gives a reception. Half of his guests are foreigners, whose official language is not french. Each guest says "bonjour" to the ambassador. And, to be polite, each guest says hello to every other guest in the official language of the person he is talking to. The french ambassador answers "Soyez le bienvenu" to every other guest. In all, 78 "bonjours" are said. HOW MANY GUESTS ARE THERE?

Answer 1

either 78 or 52

Answer 2

78

Answer 3

Say that n is the number of guest.

"bonjour" then is said n times to the ambassador.  

Every non-french person will say "bonjour"  n/2 times to every french person.  There are n/2 non-french persons.  So "bonjour" will be said (n/2)(n/2)  times more.

Every french person will say "bonjour" (n/2) - 1 times to another french person not including themselves.  And there are n/2 french person.

So "bonjour" will be said ((n/2) - 1) (n/2) times more.

n + (n/2)(n/2) + ((n/2) - 1) (n/2) = 78.

(n^2)/2 + n/2 - 78 = 0.

Using quadratic formula:

n = (-0.5 + sqrt(0.5^2 - 4 * 0.5 * (-78) ) )  / (2 * 0.5)

n = 12

There are 12 guest.

Answer 4

seventy  seven

Answer 5

My first guess - There are 52 guests.

Each guest says "Bonjour" to the ambassador - that's 52 "bonjours".

Half the guests are not French - so logically, the other half are French - that's 26 who are French.  If everyone says "Bonjour" to them once, that's 26 more "bonjours" for a total of 78...

EDIT: That's not really correct, because each French guest should receive more "bonjours" than that...

If there were 12 guests, 6 of them French:

Each of the 6 French guests would receive 11 "bonjours", (1 from each other guest) for a total of 6 x 11, or 66.

In addition each of the 12 guests would say "bonjour" to the ambassador, for 12 more "bonjours".  

66 + 12 = 78

So 12 guests total is the correct answer.

Answer 6

78?