Q23

[ShehryarB30]

Could you pls explain this

[ohthatpatrick]

The correct answer has to result in an identical game.

Answers are wrong because they're Too Restrictive (they forbid something that used to be allowed) or Too Permissive (they allow something that used to be forbidden).

As you're subjecting each answer choice to that 2-part analysis, you should ask yourself these questions:

1. Too Restrictive: as you read each rule, ask ...
- Was this true before? (if not, eliminate)
- Do I have any counterexamples to this rule? (if so, eliminate)

2. Too Permissive: as you read each rule, ask ...
- Does this "do the work" of the original rule (if so, pick it)
- Can I follow this new rule, but break the original rule? (if so, eliminate it)


A) This has always been true before. Keep it for now.

B) Our work from Q22 gets rid of this.
3 __ | 7 4 | 5 2 | 8 __

C) This has always been true. Keep it

D) This has always been true. Keep it.

E) This has always been true. Keep it.

Okay, so previous work barely helped. We have to shift to the second mindset: "Could I follow the new rule but break the old rule?" We want to see if we can follow the new rule but get 4 onto Wed or Fri.

(E) If we don't put 3 on Thu, then this rule has no power whatsoever. So let's not put 3 on Thu (which means we'd have to put it on Wed). That means we'd have to put 4 on Sat, if we're trying to break the original rule.
3 __ | __ __ | __ __ | 4 __
Can we place the rest? (3-7-5 and 2-8)
3 6 | 7 2 | 8 5 | 4 1

Let's eliminate (E).

(D) Let's put 4 on Wed or Sat. According to this rule, that puts 7 on Thu.
4 __ | 7 __ | __ __ | __ __
Oops, that won't work, because 3 - 7 - 5 will force 3 to be with 4 on Wed.

So let's try 4 on Sat.
__ __ | 7 __ | __ __ | 4 __
3 - 7 - 5 forces 5 on Fri, since it can't be with 4, and it forces 3 on Wed.
3 __ | 7 __ | 5 __ | 4 __

We still have 2 - 8, and the floaters 1 and 6. Looks like we could find happy homes for them:
3 6 | 7 2 | 5 8 | 4 1

Let's eliminate (D)

(C) If 4 - 5, then we can't put 4 on Sat, so let's try Wed.
Since 3 and 4 can't be together, we'll have to do the 3 - 7 - 5 on Thu/Fri/Sat.
4 __ | 3 __ | 7 __ | 5 __

We still have 2 - 8 and the floaters 1 and 6. Let's find some happy homes:
4 2 | 3 6 | 7 1 | 5 8

Let's eliminate (C) and pick (A).

If we had been testing (A), it would have felt like this:
Let's try putting 4 on Wed or Sat. That will force 7 to be Thu or Fri, respectively.
4 __ | 7 __ | __ __ | __ __
That doesn't work, because the 3 - 7 - 5 will force the 3 to be with the 4.

__ __ | __ __ | 7 __ | 4 __
That doesn't work, because the 3 - 7 - 5 will force the 5 to be with the 4.

Since 3 - 7 - 5 forces 7 so always be Thu or Fri,
and since we just saw that this rule doesn't let us put 4 onto Wed or Sat,
this rule will have the effect of always keeping 4 on Thu or Fri.

We've proven that this does the work of the original rule (and nothing extra), by forcing 4 to be on Thu or Fri.