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This is an Advanced Linear: Balanced, Identify the Templates game.
The game scenario and rules combine to form the following main diagram:
The game scenario indicates that laps 1 and 6; 2 and 7; 3 and 8; 4 and 9; and 5 and 10 are all paired, so that a member who swims one lap in the pair automatically swims the other lap in the pair. For example, if a member swims lap 1, he or she also swims lap 6, and if a member swims lap 6, he or she also swims lap 1. Consequently, if a member cannot swim one of the laps in a pair, he or she cannot swim the other lap in the pair. For example, the rules state that J cannot swim lap 9. By deduction, J also cannot swim lap 4.
The pairing of the laps also has an unusual effect on the last rule. The last rule is rather carefully worded to say, “At least one of J’s laps is immediately after one of O’s laps” (italics added). In a regular linear game, a rule like this would normally create an OJ block where J cannot swim lap 1 and O cannot swim lap 5. In this game, however, because laps 5 and 6 are consecutive, J can swim lap 1 and O can swim lap 5, as in the following hypothetical:
In the above hypothetical, J in lap 6 swims immediately after O in lap 5, meeting the specification in the last rule.
In the main diagram, there are several Not Laws worth considering. The last rule produces Not Laws for O on laps 3 and 8. If J cannot swim laps 4 or 9, then O cannot swim laps 3 or 8.
The third rule, M O, creates two Not Laws because the rule applies to the first lap O swims.
Hence, O cannot swim lap 1 (and lap 6) and M cannot swim lap 5 (and lap 10). And, if O cannot swim laps 1 or 6, by applying the last rule we can deduce that J cannot swim laps 2 or 7.
The only remaining Not Law is L on laps 5 and 10. If L swims laps 5 and 10, the OJ block must swim laps 2-3 and 7-8. M must then swim laps 1 and 6. The only remaining laps for K to swim are laps 4 and 9, and thus K would swim immediately before L, a violation of the first rule.
A close examination of the game reveals that the placement options of the OJ block are limited. In fact, O and J can only be placed into three separate positions: 2-3 and 7-8; 4-5 and 9-10; 5-6 and 1-10. One approach to the game would be to Identify the Templates:
Although the above templates make the game quite easy, the original setup to the game can also be used to attack the game effectively.