Extra Resistors
The master gave his young student-assistant a circuit board with 10 numbered terminals and 45 identical resistors with a resistance of 45 Ω. He instructed the student to connect each pair of terminals with a single resistor.
The student knows that after the end of the work, the master will make a quick check: he will measure resistance between terminals #1 and #2. After completing the work, the student notices that he has some "extra" resistors - pairs of terminals that he did not connect with each other.
At what maximum number of "extra" resistors has he still a chance that the master will not notice the violations?
Details and Assumptions:
The master uses a device that determines the resistance to an accuracy of 0.2 Ω.
Source: All-Ukrainian Olympiad in Physics 2017 (Grade 8, Theoretical tour, #3 by E.P. Sokolov)
The answer is 28.
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