January 13, 2008

Logic Puzzle 4

You are surrounded, and under attack! Fortunately, one of your spies stole enemy information regarding their strategy, so you know what they are going to do. Both sides have four different types of units:

A units, which always kill B Units, and always lose to everything else
B units, which always kill C Units, and always lose to everything else
C units, which always kill D Units, and always lose to everything else
D units, which always kill A Units, and always lose to everything else

When two units of the same type battle each other, both die. Your spy points out to you that you have the bare minimum number of units to kill all enemy units without any casualties, except then dies from food poisoning. You have the following map outlining enemy plans, from your spy:


a1
b1 a2
c1








d1














c1





b1
a2





b1
a2





d2

c1

d2 d2 b1

Your camp is the gray area. You can put at most one unit in each square in your territory. The enemy attacks as follows:

Each non-blank square on the outside of your base represents an enemy units that will be attacking. If they are to the right or left of your base, they will attack horizontally, and if not, they will attack vertically. The first letter for each represents what type of unit they are, and the second represents their plan. If they have a 1 next to their letter, they will engage in combat with the first unit they run into, and if they have a 2, they will sneak past the first, and engage with the second. If they never run into a first/second unit, they will flee, and not be killed. Remember that your spy says you can kill them all!

Your subordinates then ask you where to deploy the troops (the spy happened to tell them that there is no way any of them could die, so you had better make sure that this is the case). What positions do you tell them to put your units at?

EDIT: slight clarifications, just in case:

If you had:
a2 | blank | D | A | blank | blank | blank| noone
then the a2 would not encounter the D, but skip past it and attack the next unit it sees, the A in this case.

If you had:
a2 | blank | D | blank | blank | blank | blank| noone
then the a2 would escape to freedom (which is bad)!

Also, this one's pretty easy, so here are some more of the grids I came up with (I have 12 so far, so if you want more, say so in a comment):

Grid 2

b1 d2 b1 c2 a2

a1





c1








c1





d1
b1





d1
c2













b1


b2 d1
c1 a2

Grid 3


a1 b1 a2 c1

b2





d1
c2





a2
b1





d2







c1







c2
b2







c1
a2 d1 b1 a1

Grid 4


a1 b1 c1









a1
c1






d2





a2







d2
b1





a2







c2

a1 b1 c2
b2 a1

Good luck!

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