What Mr. Lister lacks in memory, he makes up with logic skills. Seriously, he can't remember anything. Can you match the six first names (Dirk, Ellen, Erik, Greg, Nelson, and Tony) with the six last names (Austin, Dunn, Ives, Lister, Newton, Sumner)?
These few memories are all that remain of his enigmatic and perhaps dramatic past:
1. When listed in alphabetical order by last name,
a)Greg comes before Dirk
b)Nelson comes before Ellen
c)Tony comes before Erik
2. When listed in alphabetical order by first name,
a)Austin comes before Newton
b)Ives comes before Dunn
c)Sumner comes before Lister
I used a chart similar to the one in described in "Analytical Solution". The chart can be filled in based on the steps that are described below to keep track of which possibilities have been ruled out. However, I have not included the chart here since it is too cumbersome to describe every step in the chart.
Aside from the individual clues given, there are 2 special cases in each alphabetical list: the 1st and last person in each list. One can remove a lot of the uncertainty for these cases.
In the last names list, Austin must be Greg, Nelson, or Tony by combining the 3 clues given (call it statement 1d). Similarly, Sumner must be Dirk, Ellen, or Erik (call it statement 1e).
In the first names list, Dirk must be Austin, Ives, or Sumner (statement 2d). But, from the previous statement (that Austin must be Greg, Nelson, or Tony), Dirk cannot be Austin. This gives simplies statement 2d to Dirk must be Ives or Sumner. Similarly, Tony must be Newton, Dunn, or Lister (statement 2e). Now, statement 1e can be modified to Austin must be Greg or Nelson because of statement 2e.
From statements 2a,2e, and the alphabetical list, Newton must be Tony or Nelson. Combining 1b, 1c, and the deduction that Newton must be Tony or Nelson, Sumner must be Erik or Ellen. This statement together with 2d means that Dirk is Dirk Ives.
Since Dirk is Dirk Ives, Greg must be Austin or Dunn from rule 1a and the alphabetical list in 1. From 1b, 1c, the alphabetical list in 1, and the fact that Greg must be Austin or Dunn, Dunn must be Tony or Nelson. This means that Greg is Greg Austin.
It was shown before that Sumner is Erik or Ellen. However, Sumner cannot be Erik because then rule 2c would be violated. Thus, Ellen is Ellen Sumner. This leaves Erik as Erik Lister. From rule 1b and the alphabetical list in 1, Tony is Tony Dunn. This leaves Nelson as Nelson Newton.
Another logical table solution (without the table)
