Barge Problem: A problem with virtual professors

A new breakthrough in virtual assistants like Siri and Alexa has enabled them to replace professors in the classroom! Although this new technology is incredibly expensive, Lafayette purchased one of these virtual assistants over the summer to teach Calculus IV, a new super-advanced calculus course. Unfortunately, it has come to light that some of these devices are broken. The broken ones always tell false statements while the non-broken ones always tell true statements.

Three students Gary, Liz and Tom are enrolled in Calculus IV. Gary asks the “professor” if it is a non-broken Siri. The “professor” answers (yes/no) but from its response Gary cannot tell what kind of machine it is.

 Liz then asks the “professor” if it is a non-broken Alexa. The “professor” answers (yes/no) but from its response Liz cannot tell what kind of machine it is. 

Finally, Tom asks the “professor” if it is a broken Alexa. The “professor” answers (yes/no) but from its response Tom cannot tell what kind of machine it is.

 From this, can you determine what type of virtual assistant is teaching Calculus IV and if it is broken or non-broken?

 

Solutions can be emailed to Professor Jonathan Bloom (bloomjs@lafayette.edu). Submissions are due by 6 a.m. on Saturday Sept. 14th.

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