Q9

[rsmorale]

What should my process be in order to solve question #9?

[giladedelman]

Great question.

I can think of two really effective approaches to solving this problem. Remember, we're looking for the maximum number of birds in the forest. So the first way we can approach it (and any similar question) is to try making the largest answer work, and working our way down from there.

So we start with (E): six. Can all six birds be in the forest? No, because we can't have H and G at the same time; they force each other out, so at least one of them has to be out.

Okay, now we look at (D): five. Can we put five birds in at once? No, again because of the H/G issue: if G is out, W is also out, and if H is out, J and M are out. So either way we have at least two birds out.

Now we want to see if four is possible. We've observed that H or G must be out, and H pushes more out, so let's keep H in and put G and W out. Who else can we keep in? Well, J, M, and S can all join H. That gives us four, so (C) is our answer!

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The other approach is to start by saying, okay, if I want to maximize the birds in the forest, who do I have to make sure I include? If I want the most people to show up to my party, who should I definitely invite? To figure that out, look at the "out" column: we can see that if H is out, it drags J and M out with it. So we definitely want to invite H to make sure J and M come. If we include H, we have to get rid of G, and W as well. That leaves only S, which we can keep.

So we've shown that four is the best we can do.


So there are two good approaches. Let me know if either of those appeal to you!

[romanmuffin]

Question: the second constraint can be written as J or M ==> H / J + M ===> H. Contrapositive: Not H ===> Not J + M / Not H ===> Not J or M. My question is, how do we know only the first contrapositive applies when we are looking at our scenarios when H is out?

[romanmuffin]

Can someone help me with the above question? I feel like the conditional statement appears often in these grouping games

[giladedelman]

Good question! Only your "second" contrapositive is correct.

Think about it: we're told that if M or J (or both) is in, H has to be in. So if H is out, can either M or J be in? No, because that would force H in! So the contrapositive of "M and/or J --> H" is "-H --> -M and -J."

Does that answer your question?