The most vital things?
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Anything that records sound like tape recorders, cameras, and camcorders. I used my cell phone and caught some startling stuff. Just becarefull because you never know what your dealing with.
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The most vital equipment is a sharp mind, well versed in physics, basic home building, plumbing and wiring, and human psychology, which critically examines everything and looks for the most likely conclusions first without letting personal bias get in the way. In addition, flashlights are good as well as video and still photography to document where you were and what you did.
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The intelligence to leave that hunt to so called professionals. Bubba, you have no idea what your dealing with you "Lil" armature!
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Sandwiches and a drink.
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A gameboy and a yo-yo you child