Which one of the following, if substituted for the condition that Waite's audition must take place earlier than the t...

Irina on October 28, 2019

@suzanne,

The game requires us to determine the order of the auditions and whether they are recorded or not. The game involves six singers - K L T W Y Z. Two of their auditions are recorded - K & L and four not recorded - T W Y Z.

R
U
__ __ __ __ __ __
1 2 3 4 5 6

The following rules apply:

(1) The 4th audition cannot be recorded, the fifth must be.

This rule allows us to infer that the fifth audition must be either K or L, and 4th is neither K nor L.

R X
U X
__ __ __ __ K/L __
1 2 3 4 5 6

(2) W audition must take place earlier than two recorded auditions.
This rule tells us that W must audition before both K & L, thus W cannot be #6. and audition #1 cannot be recorded since W (unrecorded) must precede both recorded auditions.

W > K & L

(3) K audition must take place earlier than T audition.
This rule tells us that K cannot be #6, and allows us to infer that #5 and #6 auditions cannot both be recorded because it would leave no space for T.
Combined with the previous rule, another interesting inference is that W can only be #1 and #2 since we know that #4 and #6 are unrecorded auditions, the earliest the second recorded audition could be is #2 -K or L, hence we can infer that W must be #1 or #2, and K/L (second recorded audition) must be #2 or #3.

We can also infer that if K is #5, then T must be #6 and that T cannot be #1 or #2 because T must precede K and the earliest K could be is #2.

R X
U X X X
/K/L
/W /W /K/L __ K/L __
1 2 3 4 5 6
~T ~T ~K
~W

(4) Z audition must take place earlier than Y audition.

Z> Y

This rule allows us to infer that Z cannot be #6 and Y cannot be #1. Combined with the previous rules we can also infer that #1 must be either W or Z, and #6 must be T or Y.

R X
U X X X
/K/L
Z/W /W /K/L __ K/L T/Y
1 2 3 4 5 6
~T ~T
~Y ~Z


Question six asks us which of the following if substituted for the condition that W audition must take place earlier than the two recorded auditions would have the same effect in determining the order of the auditions?

Looking back at the rules we see that this condition tells us that W can only be #1 or #2 because the other rules allow us to infer that auditions #4 and #6 are unrecorded, so the second recorded audition aside from #5 could only be #2 or #3, thus W must be #1 and or #2 respectively, and it also allows us to infer that the first audition cannot be recorded (it cannot be L/K). We need a substitute rule that captures both of these inferences. (A) tells us that Z is the only one that can take place earlier than W - what it means in practice that W is either #1 or Z is #1 and W is #2, combining both of the above inferences.

Let me know if this helps and if you have any further questions.

bb042745 on February 4, 2021

Why does B not work in the rule substitution question? W has to go 1 or 2. If W is 1, then Z is 2 and if W is 2, Z must be 1. Thank you.

bb042745 on February 6, 2021

I get it now. Space 1 is restricted to w/z; but z has some flexibility after that; e.g., W K T/Z Z/T L Y does not violate any of the rules (W-KT; W-K; Z-Y; K OR L IN 5 AND K OR L NOT IN 4)

Emil-Kunkin on January 26 at 08:42PM

We would be removing the rule that forces w to be so constrained, and only saying it must be next to Z doesn't limit W as much as the initial rule.