Alex's 4 lightbulb problem.

[bonanova]

You all know how to solve the 3 lightbulb problem, right?

Davey and the boys nodded in agreement.

OK then, said Alex, try this one.

You've got four switches that control four lightbulbs.

You can't see the bulbs - they're in a closed room.

You can do anything you want with the switches,

say they're marked 1, 2, 3 and 4, and then you can

go into the room and inspect the bulbs - they'll be

marked A, B, C and D.

A pint says you can't match the numbers and letters

correctly.

As usual, it was Jamie who took the bet.

Did Jamie get his pint?

[unreality]

Leave 1 off. The cold off bulb is A.

Turn 2 on and leave it on. The on bulb is B.

Turn 3 on and leave it on. After twenty minutes, turn on switch 4.

Twenty more minutes, turn 3 and 4 off. C is the hottest off bulb, D is the next hottest.

Am I right or is there no allowed distinction between off-but-cold and off-but-still-hot?

[bonanova]

That works. Good one!

Start with the 3-bulb solution:

[1] Turn S1 on and leave it on.

[2] Leave S2 off.

[3] Turn S3 on for 20 minutes [as good a time interval as any...] then turn if off.

Bulbs controlled by S1, S2 and S3 are respectively ON [hot], OFF [cold] and OFF [warm].

Now do something with S4 that produces a bulb perceptibly different from these three bulbs.

My choice was

[4] Turn S4 on and QUICKLY go into the bulb room.

The bulb controlled by S4 will be, uniquely, ON [warm].

It should be distinguishable from S1's bulb, not being as hot after only a few seconds of being on.