My friend Paul posed this problem to me last weekend.
“4 soldiers have been captured and buried up to their necks. 3 are in a line facing a brick wall. The fourth is on the other side of the wall. They are blindfolded and then two black and two white hats are placed on their heads. They are not allowed to talk to each other. The blindfolds are removed. If a soldier can guess what colour hat they have on, they are freed. If they guess wrong, they are killed.”
Paul’s sketch of this situation is shown below.
Which soldier, after a while, can know for sure which colour hat he has on?
5 responses so far ↓
Kate Nowak // May 22, 2009 at 8:01 pm |
Do they know there are 2 black and 2 white hats? If so I’m gonna go with the differently-hatted one on the 3-person side. He sees two white hats, so he know his must be black. Cute problem. I like the drawing.
webmaths // May 23, 2009 at 7:58 am |
Good try Kate! Unfortunately, as shown in the diagram, they are all buried facing the wall, so the middle soldier can only see the soldier in FRONT of him wearing a white hat. I gave this problem to my year 11’s and the bailed me up at the end of the class wanting to know the solution. I resisted ‘teacher lust’ and did not tell them the answer!
Denise // May 28, 2009 at 5:51 am |
What’s stupid about a logic puzzle? It’s a great way to stretch your brain “muscles” a bit. Of course, the men have to know there are 2 black and 2 white hats, or else there is no way they could figure anything out. But with that knowledge, plus being able to see what is in front of them—plus one more assumption: that they all have decent reasoning skills (not geniuses, but at least decent)—one of the men *will* be able to know his color.
Math Teachers at Play #8 « Let’s Play Math! // May 29, 2009 at 11:24 am |
[...] Speaking of logic puzzles, could you reason your way to freedom if you were one of 4 Buried Soldiers? [...]
micky( your fave student hahaha lol) // June 3, 2009 at 10:44 am |
it is the middle guy because he knows tha the guy be hind him doesnt no cause it could be a 50/50 chance and he can see that the guy in front of him is white so then he knows that he has to be black