The culture of Boojums, a species of water rat found only in Borneo, is difficult to determine because while there seem to be four social classes, one never sees more than two Boojums at one time. Based on such paired observations, anthropologists have formulated the following social laws:
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Alpha boojums are lower than betas.
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Gammas are higher than alphas.
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Deltas are lower than gammas.
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Betas are higher than deltas.
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Deltas are lower than alphas.
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Gammas are higher than betas.
Find the entire ranking of the four social classes of boojums. Also find which of the six facts above is not needed.
Solution
The ranking: gamma, beta, alpha, delta. Fact no. 3 is not needed.