#2             84. TOPCAT’S TOP HATS             


Topcat found five top hats in the dustbin: three black, two grey, and all dusty!

He then got three of the gang to sit in a line, so that Archie could see Boxer and Charlie, Boxer could see Charlie, and Charlie could see no-one.

Topcat placed a hat on each of their heads, not allowing them to see their own, or the two left over.

He then asked Archie if he knew what colour his hat was. Archie said, “No.”

Boxer was then asked if he knew the colour of his hat. He said, “No.”

Finally Charlie was asked the same question. Charlie could see none of the hats, yet he gave the colour of his hat correctly. Can you?
HINT 1

If Archie knew the colour of his hat, what doed this tell us about the colours of the hats of Boxer and Charlie?
HINT 2

If Boxer knew the colour of his hat, what does this tell us about the colours of the hats?
SOLUTION

From A’s answer we know that B and C have not both got grey hats. (Else A would have a black hat.) Therefore if C had a grey hat, B would know his own hat was black. It follows that C has a black hat.
EXTENSIONS

1. Devise a problem with just two cats sitting in a row. Too trivial?

2. Devise a problem with four cats sitting in a row. Keep in mind that you can vary the number of hats as well as the number of colours.