At the beginning of the exercise, three soldiers, named Ike, Jay and Kay, were at three different points equidistant from a target. Ike was 4 kilometers from Jay, and also 4 kilometers from Kay.

Then Jay started moving inward, directly toward the target. He stopped short of the target, at a point different from his original location, but again 4 kilometers from Ike.

At this point the distances between any two of Ike, Jay, Kay and the target were all whole numbers of kilometers.

In his new position, how far is Jay from Kay?

The problem is not solvable as stated.  As I read it, we have no idea how far Jay was from Kay at the start.  We also have no idea how far the target was.  At one extreme, the target is very far away and thus distance between Jay and Kay is almost 8km.  Jay moves almost not at all to get to the other spot and the distance changes almost not at all.

At the other extreme, the target is just past 4km, the original distance between Jay and Kay is just over sqrt(3)*4km, and the final distance is just over 4km.

Assuming that Jay is the one 4km from both Ike and Kay, the answer is 4km because the triangles (target, Jay1,Ike) and (target,Jay1,Kay) are congruent via SSS.  Then (Jay2,Jay1,Ike) and (Jay2,Jay1,Kay) are congruent via SAS, i.e. Jay is always the same distance from Ike and Kay by staying on that line.

Posted by Joel on 2006-10-09 17:37:49