1355

[gacynkar87]

P is either before M or after Q, but not both.

I chose:

M-P-Q or Q-P-M

But I don't understand why this is wrong. Could someone please explain?

Thanks!

[ohthatpatrick]

Sure thing. These "but not both" rules are tricky and VERY common on modern Ordering games.

Let's look at the way you were representing the rule:

M-P-Q or Q-P-M

Let's just examine one half at a time and compare it to the rule:

P is either before M or after Q, but not both.

M - P - Q

Okay, is P before M? No.
Is P after Q? No.

Well, it looks like we haven't followed either part of the rule. We didn't put P before M and we didn't put P after Q.

So there's no way that M - P - Q is following the rule.

What about the other half?

P is either before M or after Q, but not both.

Q - P - M

Is P before M? Yes.
Is P after Q? Yes.

Great, we must be following the rule! But wait ... the rule said that it's illegal for BOTH things to happen. One condition, but NOT the other, must occur.

The rule gives us two possible conditions "P - M" and "Q - P". It says you must follow exactly one of these.

With M - P - Q, we followed NEITHER.
With Q - P - M, we followed BOTH.

So what is the rule really giving us?

If we follow "P - M", then we are NOT allowed to follow "Q - P".

What's another way of saying "Q is NOT before P"?

"Q is after P".

So if we follow "P - M" , then we have to simultaneously have "P - Q".

Meanwhile, if we follow "Q - P", then we are NOT allowed to follow "P - M". So that means that in this world, it's "M - P".

So the two cases we have are
P is before both M and Q
or
P is after both M and Q.

Let me know if you have questions.