For a Rugby Union game, what's the smallest score that allows you to say that there must
have been at least four
(converted or not) tries?
"20" isn't the correct answer, because you could have managed it with two converted tries and two penalties. "21" isnīt it either, for three converted tries suffice, and "22" also doesnīt work, for you can manage it with less than 4 tries.
NB. The scoring is: 3 for a drop-goal or penalty kick. 5 for a try, and 7 for a converted try (A converted try is when a try has been scored, and the team that scored kicks the ball between the posts.)
(In reply to re: Big hint, almost a spoiler
Well, I didnīt give the proof, so here it goes: for any number above 19:
if the number is 3K-1, you need K-2 kicks + one try
if the number is 3K, then you need K kicks.
if the number is 3K+1. you need K-2 kicks + one converted try.
(This actually works for all numbers such that K is 2 or more, so itīs OK from 5 onwards.)