Hi — welcome and glad to have u here! —
The cross-outs are indeed because of that “not same” rule —
If we try, for example, to put three ingredients into dish 1 and three ingredients into dish 2, since there are only 4 ingredients total, there is no way to do this without using at least one common ingredient in both dishes — thereby violating the rule.
So, because of the rule that 1 and 3 have the same # of ingredients but none of the same ingredients, those dishes could either have 1 ingredient each or 2 ingredients each, but no more than that.
Beyond that, since we know the third dish uses more ingredients than the fifth, we know the third dish must use more than 1 ingredient.
Putting those two things together, what we know is that
a) the third dish must use exactly 2 ingredients &
b) those two ingredients must be different from the 2 ingredients used in the first dish.
I hope that helps clear it up, and if you have any follow-up q’s just let me know —