Math Is Fun Forum

monicao

Member

Registered: 2007-10-10

Posts: 6

Battlefield problem

This is a interesting problem...
This is a battlefield where X1 is lieutenant, X2 and O are captains, X3 is major, the forth line reprezents the colonels, X4 and X5 are generals.
Each of them can move on this disgram only horizontal or vertical (not on diagonal). Each of them cam reach out any other box if he jumps over a sequence of next pieces, vertical or horizontal. If one on them moves horizontal, he keeps his grade, if he moves vertical, he can loose a grade, or he cam win a grade.
For example, X1 can be major if he jumps over X2; then X2 can jump over X1, becoming colonel; X5 can jump over X2 and X1, becoming captain.
Find a sequence of moves so that O become a general (he have to hit line 5)!

monicao

Member

Registered: 2007-10-10

Posts: 6

Re: Battlefield problem

No ideas?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Battlefield problem

Your image file can’t be found but I found the same post by you on another forum; this is Christopher Heckman’s ASCII recreation of your diagram on www.mathkb.com.

+--+--+--+--+--+
|  |  |  |x1|  |
+--+--+--+--+--+
|  |  |  |x2| O|
+--+--+--+--+--+
|  |x3|  |  |  |
+--+--+--+--+--+
|  |  |  |  |  |
+--+--+--+--+--+
|x4|  |  |x5|  |
+--+--+--+--+--+

My gut feeling is that it can’t be done – but unfortunately I don’t have a proof.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Battlefield problem

I've been playing with this for a while, and I don't think it's possible either. I don't have a full proof yet, but this might be useful:

+--+--+--+--+--+
| X|  | X|  | X|
+--+--+--+--+--+
|  |  |  |  |  |
+--+--+--+--+--+
| X|  | X|  | X|
+--+--+--+--+--+
| X|  | X|  | X|
+--+--+--+--+--+
|  |  |  |  |  |
+--+--+--+--+--+

The marked squares on the diagram may never be entered by any soldier. If a soldier wants to go from a blank square to a marked one, there must already be a soldier in some other marked square to help it. Since the marked squares all start empty, they must remain permanently out of bounds.

Also, if soldier O wants to succeed, they need to perform at least two 'double leaps'.

---

Why did the vector cross the road?
It wanted to be normal.

Sarah12

Guest

Re: Battlefield problem

Thats Sounds fun!!!