Stupefied: Can You Solve This Festive Brain Buster?

by · January 7, 2016

Here’s an oldie but a goodie that we thought would help exercise our mental agility after a season of too much eating, drinking, and other possible debauchery. We’ll be putting a wizarding spin on the usual line-up of characters since you know… Harry Potter characters make everything more relevant. Here goes.

Dumbledore, Snape, and McGonagall are all feasting in the Great Hall and enjoying their Christmas wizard crackers (mind you, the English non-edible sort). They are busy amassing their prizes when one particularly explosive cracker ricochets and knocks Dumbledore’s glasses off. He currently cannot see.

The trio is then challenged to a game by Flitwick. Flitwick produces 5 hats from their pile of cracker presents: 3 pointed hats and 2 flowered bonnets. Flitwick ushers them into a dark room where he randomly levitates 1 of the 5 hats onto each of the trio’s heads.

They are then walked back into Great Hall where, except for Dumbledore, they could see one another but not the hat on their own head. To win the game any one of them must correctly guess what hat is on their head (pointed or bonnet).

Flitwick asked Snape if he knew, to which he replied no.

McGonagall was then asked if she knew, but again, the answer was no.

In all his wisdom, Dumbledore managed to correctly guess the hat on his head despite not being able to see.

The mystery is which hat was he wearing and how did he know? If you think you have the correct answer or arrive at your wit’s end, check out the solution below. Be sure to give it a good shot.

Solution

There are three people: Snape, McGonagall, and Dumbledore. Remember, Dumbledore cannot see. Snape goes first but doesn’t have an answer. This suggests he either saw 1 pointed hat and 1 flowering bonnet or 2 pointed hats.

McGonagall knows now that Snape could not have seen 2 flowering bonnets and deduces that, between her and Dumbledore, there is 1 pointed hat and 1 bonnet or 2 pointed hats. If they both had bonnets, then Snape would have been able to correctly guess. But he did not.

If Dumbledore were wearing a bonnet, once again, McGonagall would know that Snape had seen one bonnet and one pointed hat on the others.

Hearing the previous two’s inability to guess correctly, Dumbledore deduces that if he were wearing a flowering bonnet, one of the other two would have been able to win by now. Therefore, there is a greater likelihood that he is wearing 1 of the 3 pointed hats.

 

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