written by Isaac Asimov
published in 1969
Also a title in the Susan Calvin series.
Set in the Foundation universe
Clinton Madarian, the successor to Susan Calvin at U.S. Robots, who has just retired, initiates a project to create a "feminine" robot, which not only has female physical characteristics but will, it is hoped, have a brain with "feminine intuition". After several failures, JN-5 (aka Jane) is produced and the company plan to use it (her) to analyse astronomical data at the Lowell Observatory at Flagstaff, Arizona to calculate the most likely stars in the vicinity of Earth to have habitable planets. This will allow the most effective use of the hyperspace drive to explore those stars.
Madarian and Jane go to Flagstaff and after absorbing as much knowledge on astronomy as possible, Jane gives Madarian an answer. Mandarian and Jane board the plane that will take them back to U.S. Robots, and Mandarian calls the director of the company with the news, stating that "a witness" had also heard Jane's answer. Unfortunately, Madarian and Jane are killed and destroyed respectively in an aircrash before completing the call.
Desperate to know what, if anything, Jane had discovered, U.S. Robots asks Susan Calvin for her assistance. She solves the problem using her own version of feminine intuition - a combination of careful information gathering and astute psychological reasoning. She deduces from the timing of the call (and Madarian's propensity to call as soon as possible) that the "witness" must have been the truck driver that took them to the plane. Information provided by this truck driver enables her to reconstruct Jane's answer.