T School of Management is a management institute involved in teaching, training and research. Currently it has 37 faculty members. They are involved in three jobs: teaching, training and research. Each faculty member working with IT School of Management has to be involved in at least one of the three jobs mentioned above:
• A maximum number of faculty members are involved in training. Among them, a number of faculty members are having additional involvement in the research.
• The number of faculty members in research alone is double the number of faculty members involved in all the three jobs.
• 17 faculty members are involved in teaching. The number of faculty members involved in teaching alone is less than the number of faculty members involved in research alone.
• The faculty members involved in the teaching are also involved in at least one more job.
There are four racks numbered 1, 2, 3, 4 and four books numbered 1, 2, 3, 4. If an even rack has to contain an odd numbered book and an odd rack contains an even numbered book, then what is the position of book 4?