Can a robot pass a university math exam?

    Do androids dream of electric switches?

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    In computer math systems, such as Maple or Mathcad, a mathematical expression is entered using either a special toolbar, or using a formal language similar to LaTeX: in other words, this is how the program understands what it will have to deal with - a quadratic equation or logarithmic inequality, for example. But what about entering the text of the task in a natural language, without any conventions, and getting an answer?

    Japanese Fujitsu Laboratories in collaboration with the National Institute of Informatics (National Institute of Informatics) published a press release on the latest results of its scientific project to create an "artificial brain" named Todaiwith the long title "Todai Robot Project - Can a Robot Pass the University of Tokyo (Todai) Entrance Exam?". The ultimate goal is that Todai in 2016 should get high marks on the tests of the National Center for University Entrance Examinations, which all students take in Japan, and go to Tokyo University in 2026 formally, of course. At the same time, Todai should not "live" in something that is more or better in computing capabilities of a regular laptop.

    Strictly speaking, Todai must solve mathematical problems according to the approximate scheme presented in the figure below - as you can see, the text of the task is formulated in plain English:

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    The last time Todai was subjected to the following test - he was offered tasks of two difficulty levels (Math IA, Math II) for the entrance exam at the University of Tokyo for the humanities and natural sciences. The results were as follows: Todai successfully coped with two of the four tasks for the first block - the humanitarian one, and showed similar results for the tasks of the second block.

    Unfortunately, it is not entirely clear what this result means, but if we assume that the robot coped with half of the proposed tasks, then to some extent it turned out to be better than a significant number of living people. You can evaluate Todai's logic by its answer below:

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