raikorr: For anyone interested in the mathematics of this problem, here is a short overview. Without loss of generality, we can assume that the birch is at position (0,0), the willow is at (1,0) and the gallows are at (a,b).
Then, the first stone is at (b,-a).
The second stone is at (1-b,a-1).
Therefore, the treasure is at (1/2, -1/2).
Yuck.. math! :) ...and here's one form of the general equation..
Tx = (Bx - By + Wx + Wy) / 2
Ty = (By + Bx + Wy - Wx) / 2
..where Bx,By are coordinates of the birch, Wx,Wy the willow, and Tx,Ty the treasure. Or..
Tx = (Wx + Wy) / 2
Ty = (Wy - Wx) / 2
..if you choose the birch to be 0,0..
Now isn't this fun hehehehe? ;-)
Edit: Oh forgot! Nice way of showing it btw! +1 :-) ...and now since I know we all love this so much, here's the proof - where Sx,Sy is the starting location.
Distance from start to trees: dBx, dBy = Bx-Sx, By-Sy
(birch) and dWx, dWy = Wx-Sx, Wy-Sy
(willow) Distance from trees to stones: dBSx, dBSy = -dBy, dBx
(birch, left turn) and dWSx, dWSy = dWy, -dWx
(willow, right turn) Location of stones: BSx, BSy = Bx+dBSx, By+dBSy
(via birch) and WSx, WSy = Wx+dWSx, Wy+dWSy
(via willow) Location of treasure: Tx, Ty = (BSx+WSx)/2, (BSy+WSy)/2
...and substitution gives: Tx, Ty = (Bx-By+Sy+Wx+Wy-Sy)/2, (By+Bx-Sx+Wy-Wx+Sx)/2
..which simplifies to the above... Hmm.. maybe I should play a game instead? ;-)