# Which one of the following could be the sixth audition?

Ryan-Mahabir on December 15, 2019

Why is C correct? Why is E incorrect?

Thanks

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Irina on December 16, 2019

@Ryan-Mahabir,

Z cannot be #6 because it must take place earlier than Y per rule 4.
Please see below for the full setup:

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

We can overall see that the only possible auditions that could take place sixth are either T or Y.