« on: December 05, 2008, 11:35:14 AM »
This game is annoying because of the multiple possibilities, but it's really not so bad.. Aren't they hip, using e-mail in the topic? Next thing you know, they'll be mentioning Facebook, MySpace, and text messages.
Basically, we have either 4, 5, or 6 slots. So your templates would be:
_ _ _ _ in this template, it would be HJLH or JLHJ because we can't have LHJL (L can't be first), and first and last must be the same.
_ _ _ _ _
_ _ _ _ _ _
there are too many possibilities to draw out in the 5 and 6 slot templates. just remember to write the not-laws that L can't be first or last in each.
abstractions of the rules:
1 - HJ (horizontal block)
J is 1/2/3
L not last
1 <--> last
pick through it using the rules one at a time. straightforward - each choice except D violates a rule.
when they say "maximum," that means we should create a 6-slot template.
the key is to remember that we can only have 1 or 2 of each letter, so J and H are closer than you'd think - we get JLLHHJ
there are only 2 spaces between the first J and the first H - answer C
go back to the beginning where I wrote the two layouts for the 4-slot option: HJLH or JLHJ
what must be true is A - we only have 1 "L" in each scenario
B- could be true, not a must
C-could be true, not a must
D- could be true, not a must
E-could be true, not a must
the key here is to look at both possible layouts
E - because L cannot be 1st,it can't be last. if there is a 6th one, the 6th one must be the final one.
if the 5th is from L:
A-the 1st cannot be from J, because then the 6th would be from J. this prevents us having an HJ block because we can't have 3 Js.
B-2nd can't be from L because that leads us to HLHJLH - 3 Hs are not permitted
C-3rd can't be H because we can't fit the HJ block without making 3 of something
D- 4th from J. We get HJLJLH - answer - satisfies all conditions
E-6th from L is not permitted (see previous question, and original rule - L can't be first, so it can't be last
First try the 6 slot diagram with maximum spacing: _ L _ _ L _
however, we can't fit an HJ block except in slots 3/4, which means that there would be a 3rd slot of something, so try them closer together
HJLJLH works, but there's only one space
I'd go on to the 5-slot diagram, but since L can't be 5th in this diagram, I get
_ L _ L _ - only one space between them again, and I know that HJLJLH works, so there's only one space - the answer is B.