Another problem: a group of people lost their Passover sheep. They made one of them a messenger to find it. He found it and slaughtered it for them. But they, being afraid that he won't find the animal, got another one and slaughtered it. Which one do they eat now?
The answer: if he slaughtered his first, then it is the group's offering, and all eat from it. If they slaughtered theirs first, they eat the new one, but the messenger eats the original one because he slaughtered it for himself. What if they do not know which one was slaughtered first? He still eats his, but they cannot eat any because they do not know which one is theirs. However, since one of the two is definitely theirs - it's just that they don't know which - they fulfilled the mitzvah and do not bring it on Second Passover.
Now there is a whole group of attempts to rectify this situation by making all kinds of conditions, but none works in all life situations. The conclusion is that it is better to be silent and not fix it with all kinds of clauses.
Art: A shepherd with his flock by Anton Mauve