Sunday Times Teaser 3058 – Total Resistance
by Peter Good
Published Sunday May 02 2021 (link)
A physics teacher taught the class that resistors connected in serial have a total resistance that is the sum of their resistances while resistors connected in parallel have a total resistance that is the reciprocal of the sum of their reciprocal resistances, as shown in the diagrams. Each pupil was told to take five 35-ohm resistors and combine all five into a network. Each pupil then had to calculate theoretically and check experimentally the resistance of his or her network. Every network had a different resistance and the number of different resistances was the maximum possible. The total sum of these resistances was a whole number.
How many pupils were there in the class and what was the sum of the resistances?