16. There are 23 animals sitting in a row at the cinema. Each animal is either a beaver or a kangaroo. Everyone has at least one neighbor who is a kangaroo. What is the largest possible number of beavers in the row? So first, we cannot have more than 2 beavers next to each other and we know that because every beaver must have a kangaroo next to them and if we have 3 beavers, then the beaver in the middle will not have a kangaroo next to it. Each kangaroo should also be next to another kangaroo as the problem specifies. So let's be greedy. When we're being greedy in problems like these, you want to optimize what we're looking for which is the largest possible number of beavers in the complete row while making sure that the problem conditions are met. Let's start with a beaver because we're being greedy. We're trying to maximize the number of beavers as long as we're not breaking any rules. After this, we have to follow it with KK. Now after that, we don't need to add another kangaroo but we can be greedy again and add a beaver and then add another beaver but not more after that because there will be no Ks for the beaver in the middle. So we do BB but then after that, KK must follow again and in fact, since there are 23 seeds, we'll use this same KK BB pattern 5 times and then that gets us 10 beavers and leaves us 3 seeds. In those 3 seeds, whatever we do, we can only fit in 1 beaver and so that's going to give us our answer. The maximum number of beavers is 11 which is the answer choice D.

beavers

kangaroos

seating pattern

maximum number

BBKK strategy