Opera1: A, B, C on left; D on right

if opera1 outcome = neutral… (this means E is a star)

Opera2: A, B on left; C, E on right

if opera2 outcome = neutral… (D is a star along with E)

Opera3: D on left; E on right (outcome can’t be neutral since both D and E are stars)

if opera3 outcome = success, D and E are stars and enemies

if opera3 outcome = disaster, D and E are stars and friends

if opera2 outcome = success… (A or B or C is a star apart from E)

Opera3: A, C on left; E on right

if opera3 outcome = neutral, B and E are stars and enemies

if opera3 outcome = success, A and E are stars and enemies

if opera3 outcome = disaster, C and E are stars and friends

if opera2 outcome = disaster… (A or B or C is a star apart from E)

Opera3: A, C on left; E on right

if opera3 outcome = neutral, B and E are stars and friends

if opera3 outcome = success, C and E are stars and enemies

if opera3 outcome = disaster, A and E are stars and friends

if opera1 = success… (E is not a star)

Opera2: A, B on left; C on right

if opera2 outcome = neutral… (D is a star)

Opera3: A on left; B, D on right

if opera3 outcome = neutral, C and D are stars and enemies

if opera3 outcome = success, A and D are stars and enemies

if opera3 outcome = disaster, B and D are stars and enemies

if opera2 outcome = success, A and B are stars and friends (third opera is not needed)

if opera2 outcome = disaster… (C is a star)

Opera3: A on left; C on right (outcome can’t be success)

if opera3 outcome = neutral, B and C are stars and friends

if opera3 outcome = disaster, A and C are stars and friends

if opera1 = disaster… (E is not a star)

Opera2: A, B on left; C on right

if opera2 outcome = neutral… (D is a star)

Opera3: A on left; B, D on right

if opera3 outcome = neutral, C and D are stars and friends

if opera3 outcome = success, B and D are stars and friends

if opera3 outcome = disaster, A and D are stars and friends

if opera2 outcome = success… (C is a star)

Opera3: A on left; C on right (outcome can’t be disaster)

if opera3 outcome = neutral, B and C are stars and enemies

if opera3 outcome = success, A and C are stars and enemies

if opera2 outcome = disaster, A and B are stars and enemies (third opera is not needed).

Thus, all 20 possibilities are covered by 3 operas – 10 where the two stars are friends, and 10 where they are enemies. In other words, each combination results in a different “signature” of 3 outcomes. For example, if B and C were the stars and they were friends, then the outcomes would be success, disaster, neutral. On the other hand, if B and C were the stars and they were enemies, the outcomes would be disaster, success, neutral.

]]>Andrew

Founder of https://mathtutorpro.com/

]]>Andrew

Founder of MathTutorPro.com

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