Question 1194870
In the first 4 months of 2023 we have 120 days. We want to have at least 120 groups of 3 guests, so each group is invited only once.
The number of groups formed with 3 friends out of n, is n over 3 which equals:
n!/[3!(n-3)!]= n*(n-1)*n(-2)/6

we request that  
n*(n-1)*n(-2)/6>=120 
10*9*8=720 therefore n=10