Answers to last issue's Brain Teasers

1. Which switch?
There is a lamp inside a photography darkroom. When the darkroom door is closed, it is impossible to tell from outside the room whether or not the lamp is on. There are two switches outside the door of the darkroom.  One or both of the switches may control the lamp. It also could be that neither of the switches control the lamp. All you know is that the light bulb is currently off and that the lamp and bulb are in working condition. The darkroom door is closed and once you open the door you cannot touch either of the switches. If you can only open the dark-room door one time, how can you tell which switches, if any, control the lamp?

Answer: This has an unusual answer, but it works fine in practice! Turn the first switch on and leave it on for ten minutes. After ten minutes, turn that switch off and turn the second switch on. Open the darkroom door, and lightly (in case it is hot) touch the bulb. If the lamp is on, and the bulb is quite hot, both switches work the lamp. If the lamp is on, and the bulb is cool, the second switch controls the lamp. If the lamp is off, and the bulb is hot, switch one controls the lamp. If the lamp is off, and the bulb is cool, neither switch controls the lamp.

2. Who's first?
Four athletes, Anu, Brinda, Carol, and Dhanush went out one morning and ran a race. At the end of the race, the following statements were made: 
Anu: "I didn't come in first or last."
Brinda: "I didn't come in last."
Carol: "I was first."
Dhanush: "I was last."
It is known that one, and one only, of the four athletes is lying. Who won the race?
Answer: The simplest way to proceed is to test out each case. Only one person was lying, and we can check the possibility of each being the liar in turn. Only one case will come out without contradiction.
Let us start by assuming Anu was lying. Then Anu must be either first or fourth. But then Carol and Dhanush are both telling the truth (only one person lies) and they maintain they came first and fourth. So this is not possible, or Anu is not the liar.
Let us make Brinda the liar. Then she did come in fourth (last) but Dhanush who is telling the truth also came in last. Again we have a contradiction.
If Carol is lying, then she could not be first. Then since the other claim they did not win, only Brinda could be the winner. Dhanush who is telling the truth is last, and Anu and Carol are second and third (we don't know which was second and which was third). But certainly Brinda is the winner.
You can check that Dhanush is not the liar, because then all the others (truth-tellers) claim they were not last, and neither is Dhanush. This means no-one came last and this is not possible.
3. For Fun
Two police-men were parked along a one-way street looking for traffic violators. They spotted a taxi driver going in the wrong direction, yet they did nothing. Why?
Answer: The taxi driver wasn't driving at the time, he was walking. So he wasn't doing anything wrong! (Well, I told you it was for fun!)