## 4 Buried Soldiers

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?

I have been teaching Mathematics in Victorian secondary schools for 30 years. I use the www to make my maths lessons better. I hope this blog will give other teachers some ideas to try in their own classes.
This entry was posted in Problem Solving and tagged , , . Bookmark the permalink.

### 9 Responses to 4 Buried Soldiers

1. Kate Nowak says:

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. 🙂

2. webmaths says:

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!

3. Denise says:

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.

4. micky( your fave student hahaha lol) says:

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

5. pupil in depress says:

6. pupil in depress says:

I REALLY NEED TO KNOW !!!!!!!!

7. Olivia (year7) says:

Its the one in the middle because he knows that the one on the end can see him and the one in front of him so seeing the one infront of him is white he knows he is white 😀

8. Mohd. Arham says:

1 | 2 3 4

it has two solutions

case 1st :
1 | 2 3 4
w b b w

the no. 4 will kno as he has same color hats on 2 and 3.

case 2nd:
1 | 2 3 4
w b w b (i.e 2 and 3 have different color hats)

then 4 will be confused as (50-50)—-he will not answer
but after waiting for some time
3 realizes that 4 is confused(50-50….) and this is only possible when 2 and 3 have different hat color……
then 3 will reply ‘opposite’ color that 2nd hat.