The Islands of the Cartesian Sea

Captain Cauchy has six sails on his ship. Each lets him travel from (x,y) to either (x+a, y+b) or (x-a, y-b) in a single day, where a and b are integers specific to the sail. Captain Cauchy never stops at the same island twice, except when he visits his island of origin.

Captain's log:

• Day 0: Set out on my search for a treasure to give to Piglet.
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• Day 2: Forgot to bring rum. Returning to home base.
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• Day 6: Setting out again with a large supply of rum.
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• Day 10: No luck here. Let's try a different quadrant.
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• Day 15: First mate seasick. Returning home.
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• Day 16: Found replacement first mate. Venturing out again.
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• Day 20: No treasure, but there's another island in the same direction. Let's keep going.
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• Day 22: Still no treasure.
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• Day 25: After lots of rum, forgot how to add vectors. Returning home to find mathematician.
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• Day 26: Kidnapped a grad student. Venturing out again.
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• Day 30: Nothing here.
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• Day 32: Found treasure at unlucky coordinates. Returning home.
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