The treasure map without the gallows
An old map says: "On the island stand an oak, a pine and a gallows. Walk from the gallows to the oak, counting your paces; at the oak turn right by a right angle and walk the same number of paces; drive in a spike. Return to the gallows, walk to the pine counting paces; at the pine turn left by a right angle and walk the same number of paces; drive in a second spike. The treasure lies halfway between the spikes."
You arrive to find the oak and the pine, but the gallows has rotted away without trace.
Can you still find the treasure? Where is it?
Show a hint
Try it with the gallows in two different imagined positions and see whether the treasure moves. Coordinates, or complex numbers, make the algebra one line.
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