# Another Game -- Exam 33, sec 4, #9 (forest)

#### nemo

##### Another Game -- Exam 33, sec 4, #9 (forest)
« on: September 08, 2005, 07:09:06 PM »
I'm having some trouble setting this one up. Your help is much appreciated!

Bird-watchers explore a forest to see which of the following six kinds of birds -- grosbeak, harrier, jay, martin, shrike, wren -- it contains. The findings are consistent with the following conditions:

If harriers are in the forest, then grosbeaks are not.
If jays, martins, or both are in the forest, then so are harriers.
If wrens are in the forest, then so are grosbeaks.
If jays are not in the forest, then shrikes are.

9. Which one of the following is the maximum number of the six kinds of birds the forest could contain?
a) two
b) three
c) four
d) five
e) six

#### kmanista

##### Re: Another Game -- Exam 33, sec 4, #9 (forest)
« Reply #1 on: September 09, 2005, 12:46:37 PM »
Condition (1) says harriers OR grosbeaks, but not both.  So we can't have more than 5.
Condition (2) indicates that harriers "go with" more birds, so let's test with that first.

Harriers, jays, martins, (can't have wrens, because can't have grosbeaks), shrikes (Condition (4) doesn't seem to exclude both jays and strikes, if I'm reading it right).  That gives us 4.

Grosbeaks (no harriers, no jays, no martins), wrens, shrikes.  That gives us 3.

So C is our answer -- no more than four birds can be in the forest.