Which of eight switches runs the pump?

Question

A panel has eight identical switches. Exactly one of them powers a hidden pump: when that switch is flipped up, the pump runs; the other seven switches do nothing at all. You can set any switches up or down in any pattern, and after each setting you can see a single indicator that tells you only whether the pump is running or not. What is the fewest number of indicator checks that guarantees you can identify the live switch, and how?

Accepted Answer

The answer is three checks. Each check gives one bit of information (pump on = the live switch is somewhere in the "up" group; pump off = it's in the "down" group), so you can halve the suspects every time. Number the switches 1 through 8. Check 1. Flip switches 1, 2, 3, 4 up and 5, 6, 7, 8 down. - Pump on → the live one is among {1, 2, 3, 4}. - Pump off → it's among {5, 6, 7, 8}. Either way you're left with 4 suspects. Check 2. From the surviving four, put two up and two down. The indicator tells you which pair contains the live switch, leaving 2 suspects. Check 3. From the surviving two, fl…

Which of eight switches runs the pump?

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