Mystery Master	Analysis of New Self-Improvement Committee	Member

This five-star logic puzzle has 5 noun types, 10 nouns per type, 7 links, 111 facts and 6 rules, where rules 1, 2, 4, 5, and 6 incorporate triggers. There are 1000 marks and 10 grids.

Levels 1

Level 1 contributes 843/1000 marks and 56/100 pairs, all by level 1a. All but rule 3 has been invoked at least once. The following 8 facts have yet to be fully examined.

Facts

88. Before lunch, the one in purple did not sit directly across from the one in brown.
89. After lunch, the one in purple did not sit directly across from the one in brown.
92. After lunch, Karen did not sit next to Judy.
93. After lunch, Karen did not sit next to Pam.
94. After lunch, Karen did not sit next to Shelli.
95. After lunch, Karen did not sit next to Susan.
103. After lunch, Susan did not sit next to the one in green.
106. After lunch, Susan sat directly across from Freeman.

The seats across from each other are 1 and 6, 2 and 10, 3 and 9, 4 and 8, 5 and 7. For fact 88, before lunch, purple can be in seats 3, 5, 7, 9, and brown can be in seats 7, 9. For fact 89, after lunch, purple can be in seats 3 - 6, 8, 9, and brown can be in seats 3 - 5. So both facts are still needed.

For fact 92, after lunch, Karen can be in seats 4, 6, 8, so this fact is satisfied.

For fact 93, after lunch, Pam can be in seats 8, 9, so this fact is still needed.

For fact 94, after lunch, Shelli can be in seats 3, 4, 5, so this fact is still needed.

For fact 95, after lunch, Susan can be in seats 3, 4, so this fact is still needed.

For fact 103, after lunch, the one in green can be in seats 3 - 6, so this fact is still needed.

For fact 106, after lunch, Freeman can be in seats 8, 9, so this fact is still needed.

Level 2

Level 2 solves the puzzle. Level 2b examines fact 93 "After lunch, Karen did not sit next to Pam." After lunch, Karen can be in seats 4, 6, 8 and Pam can be in seats 8, 9. So Level 2b answers the questions "If Karen is in a seat, can Pam be in any seat where she is not next to Karen?" and "If Pam is in a seat, can Karen be in any seat where she is not next to Pam". Some of the process is given below.

1. If Karen is in seat 4, can Pam be in any seat that is not next to her? Yes (8 or 9).
2. If Karen is in seat 6, can Pam be in any seat that is not next to her? Yes (8 or 9).
3. If Karen is in seat 8, can Pam be in any seat that is not next to her? No! Thefore, Karen cannot be in new seat 8 (mark 844).

This level also examines fact 94 "After lunch, Karen did not sit next to Shelli." where Karen can now be in seats 4, 6, and Shelli can be in seats 3, 4, 5. Some of the process is given below.

1. If Karen is in seat 4, can Shelli be in any seat that is not next to her? No! Therefore, Karen cannot be in new seat 4 (mark 887).

This level also examines fact 103 "After lunch, Susan did not sit next to the one in green.", where Susan can be in seats 3, 4, and green can now be in seats 3 - 5 (mark 884 eliminated 6). Some of the process is given below.

1. If Susan is in seat 3, can green be in any seat that is not next to her? Yes (5)
2. If Susan is in seat 4, can green be in any seat that is not next to her? No! Therefore, Susan cannot be in new seat 4 (896).

What is important to note here is that for any fact where the link is not "with", the two nouns in the fact can never be together.

All that's left is to determine the last names of Brian, Frank, and Karen. Brian can be Smith or Strom. Frank can be Smith, Snow, or Strom. Karen can be Smith, Snow, or Strom. Rule 3 states "Snow sat next to Strom either before or after lunch." They cannot sit next to each other before lunch, so it must be after lunch. Snow can be in seats 6 and 8, while Strom can be in 5, 6, 8, so Snow must be in 6 and Strom must be in 5.

Rules

Here are the rules for this puzzle. All but rule 3 has been invoked at least once.

1. After lunch, no one sat next to a person they had sat next to before lunch.
2. Ms. Karnell sat next to the one in green either before or after lunch.
3. Snow sat next to Strom either before or after lunch.
4. After lunch, the one in yellow had moved one chair to his right.
5. After lunch, the one in white did not sit where the one in black had sat.
6. After lunch, the one in white did not sit where the one in orange had sat.

For rule 2, before lunch Ms. Karnell sat in seat 7 and the one in green sat in seat 2, so they must sit next to each other after lunch. After lunch, Ms. Karnell can sit in seats 3 - 5, and the one in green can sit in seats 3 - 6.

For rule 3, before lunch Snow can sit in seats 5 and 10, and Strom in seats 2, 5, and 10, so they must sit next to each other after lunch. After lunch, Snow can sit in seats 3 - 6, 8, 9, and Strom in the same seats.

Rule 4 has been satisfied since the one in yellow sat in seat 8 before lunch, and in seat 7 after lunch.

For rule 5, the one in black sat in seat 6 before lunch, so the one in white can not sit in seat 6 after lunch. So this rule has been satisfied.

For rule 6, the one in orange sat in seat 4 before lunch, so the one in white can not sit in seat 4 after lunch. So this rule has been satisfied.

Analysis

Before lunch, the one in purple can be in seats 3, 5, 7, 9; the one in brown can be in seats 7, 9. Because of the facts, the combinations that do not work for purple and brown are 3 and 9, and 5 and 7.

After lunch, the one in purple can be in seats 3, 4, 5, 6, 8, 9, and the one in brown can in seats 3, 4, 5. Because of the facts, the combinations that do not work for purple and brown are 8 and 4, and 9 and 3.

After lunch, Karen did not sit next to Judy, Pam, Shelli, and Susan. Karen can be in seats 4, 6, and 8, so she definitely can't sit next to Judy. Pam can be in seats 8 and 9. Shelli can be in seats 3, 4, and 5. Susan can be in seats 3, 4. The one in green can be in seats 3, 4, 5, 6, 8, and 9. And Freeman can be in seats 8, and 9.

Where Did Karen Sit After Lunch?

If Karen is in seat 4, the other girls cannot be in seats 3, 4, 5. This means there are no possible seats for Shelli and Susan, so Karen cannot sit in seat 4.

If Karen is in seat 8, then the other girls cannot be in seats 7, 8, 9. This means there are no possible seats for Pam, so Karen cannot sit in seat 8. Therefore, Karen must sit in seat 6. Entering this mark brings the totals to 889/100 marks and 64/100 pairs.

Where Did Susan Sit After Lunch?

Susan can sit in seats 3 or 4. If we attempt to place Susan in seat 4, the program comes back with a contradiction, so Susan must be in seat 3. This gives us 968/1000 marks and 88/100 pairs.

For rule 2, before lunch Ms. Karnell sat in seat 7 and the one in green sat in seat 2, so they must sit next to each other after lunch. After lunch, Ms. Karnell sat in seat 4, and the one in green sat in seat 5, so rule 2 has been satisfied.

For rule 4, before lunch the one in yellow sat in seat 8, and after lunch in seat 7, so rule 4 has been satisfied.

For rule 5, before lunch the one in black sat in seat 6, so after lunch the one in white cannot sit in seat 6. After lunch, the one in white can is in seat 9, so this rule has been satisfied.

For rule 6, before lunch the one in orange sat in seat 4, so after lunch the one in white cannot sit in seat 4. After lunch, the one in white can is in seat 9, so this rule has been satisfied.

For rule 3, before lunch Snow can sit in seats 5 and 10, and Strom in seats 2, 5, and 10, so it is not possible for them to sit next to each other before lunch. After lunch, Snow can sit in seats 6 and 8, and Strom in 5, 6, and 8. Therefore, after lunch Strom must be in seat 5, and Snow in seat 6. This rule has been satisfied. And we have the solution!

The rules in this puzzle allow it to be solved without needing to make assumptions.