Occasionally I am asked to take a group photo.
Every time I am choosing the best (or even usable) photo from the set,
I am struggling with finding one. The reason is that at any given moment someone takes less then the best pose, facial expression, ... So, you end up with one photo where it's better for one person, and another one for another person...

So, I've been thinking about some empirical formula for the number of photos I need to take to ensure I could choose one where everybody is OK. When I have 1 person, the first photo will be bad, so, I need to take an extra (or two). So,
for 1 person:  1+1 (or 1+2) photos.
For 2 people I will have about two bad ones (one for each), so, 2+1 (or 2+2).

One might think that for N people, I'd need N+1 (or N+2)...
But that's wrong, because in addition to everybody having individual bad moments, I will have a combination of bad poses in more then one person, plus, people getting distracted when the crowd grows close to 10 and above. The deduction and combinatorics does not seem to work well here, but I suspect that statistically, I'd need N^2+1 or even N!+1 (where N!=1*2*3*...*N) to optimize the probability of finding one photo where everybody looks fine.



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