Child, Blocks, Cabinet, Questions.

For the answer to Friday’s Challenge, let’s take a look at the game reprinted here, followed by detailed explanations for all of the moves shown below.

You’ll see that I’ve symbolized each rule individually, then combined them.  It’s in this combination that I get the most mileage out of my rules – as we’ll see, many of the questions can be answered simply by counting the things ahead of or behind any given element within our chain.  Also, note that only G or M could be the first block put in; every other block has at least one block ahead of it.

Now, the questions.

Number 1 is our accounting question.

(A) I is not after G.  Get rid of it.

(B) J is not before F.  Wrong.

(C) F is before M.  Bad.

(D) G is after K.   Out of here.

That leaves us with only (E).

Number 2 lets us use that chain of rules:

(A) L must have at least 3 blocks ahead.

(B) G must have 6 blocks behind.

(C) F must have G, I, J, and M ahead of it.

(D) Sure; why not?

(E) Nope – J must have 3 blocks after it.

Number 3 puts M 7^th, which means F is last and G must be first (nothing else could be first).

(A) G is first.

(B) Use your list – I must have J, L, H, and in this question also M and F behind it; therefore, it cannot be any later than 3^rd.

(C) Sure; why not?

(D) J could not be that late under any circumstances.

(E) No – F must be last if M is 7^th.

Question 4.  Place I in 4^th, then use that chain – J must be after I, with L, H, and F after it.  That means it must be 5^th.  G, K, and M must then appear in some order in the first 3 spaces.

(A) Could be, but doesn’t have to be.

(B) Could be, but again doesn’t have to be.

(C) Same as (A) and (B).

(D) Yep; this is what we knew to be true.

(E) Mebbe.  Then again, mebbe not.

Question 5 gives us F in 5^th and asks what must be false.  Lots of wiggle room, but K, L, and H must be the three blocks after F (everything else has to come before it, via our chain of rules), with G, I, and J in that order, and M somewhere in those first 4 slots.

(A) M could be first, followed by G, I, and J.

(B) Or you could have G, I, J, M.

(C) Ditto (B).

(D) Nope.  K is 6^th, 7^th, or 8^th.  No way is K 4^th.

(E) L could be any of the last 3 blocks.

Question 6 has J somewhere before M.  Two ways we can deal with this; run through answer choices with this modification to our chain, or else plot what we know in our diagram.  I’ll walk through the latter (you can do the former on your own, kiddo).  If M is after J, then J has almost everyone behind it – G and I must be ahead of it, and maybe K is also.  If those three blocks are ahead, J must be 4^th, with M, F, L, and H in some order after it.  If K is behind J, then J must be third, with G and I in 1 and 2 respectively, and the other 5 blocks behind in some order.

(A) Nope.  G is 1^st either way.

(B) Unh-uh.  I is 2^nd or 3^rd.

(C) No; F can not be earlier than 5^th under any circumstances.

(D) Nope; we’ve already shown that J is either 3^rd or 4^th.

(E) Sure; why not?

And you see?  This is why we call them Games.

See you Wednesday.