Sorting Resistors Puzzle
An engineer ordered 9 boxes of 100-ohm resistors and a box of 110-ohm resistors.
All 10 boxes arrived with 10 resistors each,
but both the boxes and the resistors were unmarked.
The engineer needs to find which box has the 110-ohm resistors.
He has an ohm meter to measure resistance.
How can he find the 110 box with the fewest resistance measurements?
Label the boxes, “1”, “2”, …, “10.”
Connect in series, 1 from 1st box, 2 from 2nd, and so on till 10 from 10th box.
Measure the resistance (M) of this series of 55 resistors.
If all 55 were 100 ohms, then M = 100*(1+2+…+10)=5500.
We find the box of 110-ohm resisters from this one measurement as
Box = (M-5500)/10.
The measured resistance R will only be 10 ohms larger that 5500 if the first box contains 110-ohm resistors.