# 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?**

**Solution:**

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.