A cube of pure tungsten, 1000 feet wide on each side, sits flat in the middle of a grassy field on Earth. The owner of the field wishes to sell the tungsten. What is the most cost effective method, using existing technology, of bringing this tungsten to market? Note that tungsten has limited commercial value in the form of monolithic cube: it must be broken into pieces.

Do not concern yourself with the issue of the tungsten's actual market value, or the fact that the price of tungesten will likely go down dramatically over the course of this mining project. This question is just about how to most easily and cheaply chop up this big hunk of tungsten.

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    $\begingroup$ A 1000ft cube of tungsten weighs more than all humans combined, is 7 times denser than rock, and more than twice as tall as the Great Pyramid of Giza. It ain't going anywhere but down. Source: Wolfram Alpha. $\endgroup$ – John Dvorak Feb 17 at 22:59
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    $\begingroup$ Assuming that the extremely heavy cube of tungstem is somehow magicked to stay above ground, then cutting pieces of it becomes a simple engineering problem. Machine tools able to cut tungsten are commercially available. The specialists at Mitsui Seiki will be happy to provide solutions for all your tungsten cutting needs. $\endgroup$ – AlexP Feb 17 at 23:05
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    $\begingroup$ Here's a thought. There's a good chance it won't just dip below the surface. It will dip below the surface, submerge entirely under the grassy field, continue pushing aside all of the rock below it, then continue through the liquid bits, and straight to the core. The good news is, its mass is negligible compared to that of the core itself so Earth's magnetism wouldn't be affected. The bad news is, you can't sell it. Seismologists across the globe should get some very interesting data from the event, though. $\endgroup$ – John Dvorak Feb 17 at 23:17
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    $\begingroup$ I understand pure tungsten is rather brittle, so just whack it with a sledgehammer to break off chunks. If you want more, jackhammers, wrecking balls, and such should work. If you don't have access to sophisticated machine tools, you could look at how diamond cutting blades for stone & ceramic tile work. $\endgroup$ – jamesqf Feb 18 at 4:50
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    $\begingroup$ @JohnDvorak It will surely sink in a good bit but I'm not sure whether it could sink in completely into the earth. The friction involved in pushing earth so far to the sides is quite high. How far would it sink seems like an interesting separate question where I don't know what physical model to apply. $\endgroup$ – quarague Feb 18 at 11:55

In my opinion, the most cost effective way (and easiest way) would be to have your clients mine it.

Instead of selling them the extracted material, you sell them the rights of extraction. Your clients would most likely become mining companies (instead of the manufacturers) interested in turning a profit themselves, but they wouldn't just do the work for free, they would pay you in order to mine it.

That would be the cheapest way to sell it. It might not be the one that gets you the most money in the end, but it's extremely cost effective (being your cost zero, any $ you make is 100% profit) and doesn't require any equipment on your part, other than a few pieces of paper and a pen (for the contracts).

Hope this helps.

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I'm remembering that tungsten can burn under the right conditions.

So you start with thermite. You scratch a small hole and load it up with thermite. It burns a hole that stops burning when it dies from lack of oxygen because the hole is deep, or the block carries too much heat away. Tungsten smoke! Don't breathe this!

With some experimentation you find out that you can line the hole with an oxidizer mixture that will give up oxygen to the tungsten when heated. You should be able to control the burn fairly well. If you want to burn in this direction, load that direction with more oxidizer.

You burn a few strategically located holes to leave a convenient sized chunk relatively easy to remove. It wastes quite a bit of tungsten. And it produces a lot of pollution in both gas and solid form.

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