You and your buddy have each woken up at some random, unknown point in the milky way galaxy.

You have a very bright, omni-directional beacon that can easily be seen from any point inside it's light cone.

You can travel in any direction, at any speed up to C (but not exceeding it of course).

Your goal is to locate and rendezvous with your buddy for one last drink, sometime before one of you dies of old age.

What's your strategy.

--other answers were wrong (or Dyer posed it wrong) since problem statement says only you, not you buddy, can move, and only you, not buddy, have beacon. Also, the beacon seems not useful unless you get within a few light years of buddy, otherwise he'll never see it before dies of old age. Also, if you are more than 100 lightyears from buddy then even if you travel at C he'll die before you reach him. Also, Goucher's brownian motion solution is technically wrong in the sense brownian motion has infinite path length so even if you travel at C and do not mind infinite acceleration, you'll still never get anywhere. So anyhow... as posed, there is no solution. If however Dyer really meant BOTH you & buddy can move then: cover the galaxy with a wireframe grid at grid spacing 1 meter (say) then traverse all wires in the grid at speed C while buddy does same on his grid. Continue until you collide. (Assume you both wider than 1 meter.) No beacon needed, but easy to avoid collision by using...