I have a partial packet, maybe 1/3 of dry Nottingham yeast leftover - I had used it to prime beer that I had sitting in secondary for quite a while. Could I just use this amount here to create a viable starter, maybe adding an extra day to get the cell count up?
You can't be a real country unless you have a beer and an airline - it helps if you have some kind of a football team, or some nuclear weapons, but at the very least you need a beer.
Yes, in fact dry yeast tends to die off when opened for more than a few days, so it's a good idea.
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