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An elementary school class tried feeding apples, broccoli, cucumber, hay, and lettuce to a guinea pig and a rabbit. When given any two of these foods, each animal clearly and consistently preferred one over the other:
Base on the information, select for Guinea pig's favourite a pair of foods such that either might have been the guinea pig's favourite and select Rabbit's favourite a pair of foods such that either might have been the rabbit's favourite. Make once two selections, one in each column.
Apples or hay
Broccoli or lettuce
Cucumbers or broccoli
Hay or cucumbers
Lettuce or apples
Guinea Pig Preferences:
Rabbit Preferences:
What CANNOT be favorites:
The key insight is that the cross-references between favorites create constraints:
We need to identify pairs where each animal's favorite could be either food in that pair.
From guinea pig's preferences:
Could guinea pig's favorite be hay?
Could guinea pig's favorite be apples?
Could guinea pig's favorite be cucumbers?
Could guinea pig's favorite be broccoli?
Could guinea pig's favorite be lettuce?
Conclusion: Guinea pig's favorite must be either hay or apples
From rabbit's preferences:
Could rabbit's favorite be lettuce?
Could rabbit's favorite be broccoli?
Could rabbit's favorite be cucumbers?
Could rabbit's favorite be apples?
Could rabbit's favorite be hay?
Conclusion: Rabbit's favorite must be either lettuce or broccoli
Multiple valid configurations exist depending on how the preference chains connect. The constraints allow for flexibility in the exact rankings while maintaining the required relationships.
The cross-referential constraints (each animal's preference involving the other's favorite) create a web of dependencies that limit possible favorites while still allowing multiple valid configurations.
In TPA questions with preference chains: