Joining two ropes together:
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The Zeppelin Bend

End loop:
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The Anglers Loop

Adjustable loop:
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The Tautline Hitch. This is certainly not the best sliding loop available, but you said I had to be able to tie it behind my back, with my eyes closed, in the rain!

There's a whole lot of other useful knots, but you limited it to three! Didn't even get into the hitches or stopper knots - maybe you should expand your rules to "five or six knots".