These puzzles involve looking at the problem from an unexpected viewpoint – sometimes known as ‘lateral thinking’.

The Barrel

There is a barrel with no lid and some beer in it. “This barrel is more than half full of beer,” said Chuck. “No it’s not,” say Joe. “It’s less than half full.” Without any measuring implements and without removing any beer from the barrel, how can they quickly and easily determine who is correct?

Switches

Three switches outside a windowless room are connected to three light bulbs inside the room. How can you determine which switch is connected to which bulb if you are only allowed to enter the room once?

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Answers below:

The Barrel

There is a barrel with no lid and some beer in it. “This barrel is more than half full of beer,” said Chuck. “No it’s not,” say Joe. “It’s less than half full.” Without any measuring implements and without removing any beer from the barrel, how can they quickly and easily determine who is correct?

Answer

My initial answer was to assume that the barrel symmetrically bulged and if you placed it up against something vertical, the point of contact marked the half-way point. But this is too awkward. The simple answer is tip the barrel until the beer reaches the rim. If you can see the bottom, then the barrel is less than half full; otherwise not.

Switches

Three switches outside a windowless room are connected to three light bulbs inside the room. How can you determine which switch is connected to which bulb if you are only allowed to enter the room once?

Answer

Say you have left (L), middle (M) and right (R) switches outside. If you turn L on, you know that the light that is on in the room corresponds to L. But what about the other two lights? To answer this you need to think laterally – about properties of lights. Turn M on for a couple of minutes, then off. Then go in the room, and feel the two light bulbs that are off. The warm one corresponds to M, the cold one to R!