- #1

Lancelot1

- 28

- 0

I am trying to solve this one:

John has n friends . He wants to invite in each evening (365 days a year) three of his friends for dinner. What should be the size of n, such that it will be possible not to invite the same triplet twice ?

What I did was:

\[\binom{n}{3}\leq 365\]

which turns into:

\[\frac{(n-1)(n-2)n}{6}\leq 365\]

I have tried to solve it, manually and with a mathematical software, in both ways n was not a natural number...where is my mistake ?