I think the cold beer trick isn’t that original to anyone who has made ice cream. Adding salt to ice lowers the freezing point, so it has to melt. Melting (a change of state) requires it to absorb heat which cools the beer faster than mere ice alone.
Personally, I find that a rigid rotation system, wherein one always replaces a cold beer with a warm one, works great. As long as you maintain a first-in, first-out rule, you will always have cold beer. Of course, the guests sometimes find my mandatory pre-party procedural indoctrination a little annoying, but if the beer is free…
Regarding the beer trick. We used to do this all the time. Its a Minnesota tradition. Ice water can get to 33 degrees. Ice water with salt in it can get to 25 degrees. U can also roll a beer is snow for about 2 minutes and it will get good and cold. Mythbusters once tackled this story.
A bit of useless information: The salted-water-below-freezing trick is the basis of the Farenheit scale. Back when the coldest thing in the world was ice someone noticed that salted water was liquid when ‘fresh’ water froze. Then someone invented a mercury thermometer and they could start to actually measure stuff; they needed a high and low number to act as the basis of a scale. So they said, let the coldest liquid water–heavily salted and just before it freezes– make Zero. And human beings are pretty much the same temp unless we’re sick so ‘normal’ human temp became 100. There you have the F scale.
Centigrade came much later (French Revolution, Napolean, all that) and they had better thermometers. Their scale used the temp of freezing fresh water for Zero and the temp of boiling fresh water is 100.
Three minutes to cool down beer that way? I guess so. However, as I would have likely had a few beers before even starting this, I think it would likely take me 5-10 minutes to dig out the big pot, another 5 minutes to find the measuring cup and pour out the salt, another 10 minutes to actually set up and mix, then a few more minutes to clean up. Probably be faster to just stick the beer in the ice tray in the freezer for a half hour.