Can you find the treasure?? My big bro gave this problem one week ago. I could not still solve it.Please HELP. **STORY** A man was just looking for items in his store room. Suddenly he found a map , which showed  to house A and turns 90* and moves to M such that PA=AM. Similarly if he goes from P to B and turns 90* again to move from B to N such that BN=PN THEN a straight line MN is produced.In the midpoint of MN the TREASURE IS PRESENT.  was cut down (i.e the pole was absent from the place) **_NOW CAN HE FIND THE TREASURE????_** thanks in advance!!

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As the diagram suggests, any starting point and the endpoints ($A^\prime$ and $B^\prime)$ of the routes through $A$ and $B$ determine pairs of congruent triangles with the (other) vertices $X$ and $Y$ of the square with diagonal $\overline{AB}$. The key midpoint property then becomes clear (and nicely related to the distance from starting point to square-corner).

Now, starting at any point on the $Y$ side of $\overleftrightarrow{AB}$, the instructions (with appropriately-oriented turns) take you to $X$ (necessarily the midpoint of $\overline{A^\prime B^\prime}$); and vice-versa. (What about points _on_ $\overleftrightarrow{AB}$?) So, you should check both points, just to be sure. $\square$