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What does "at least one" mean in mathematics?
At least it illustrates the bottom line. Generally speaking, at least when you notice that she must have follow-up restrictions, such as the word "must".

There are 9 socks of three colors in a cloth bag, take out 1 sock at a time. How many socks can you take out at least to ensure that there are 2 pairs of socks with different colors? This "at least" means that when you take out at least more socks than this, you can certainly meet the requirement of "having 2 pairs of socks with different colors". As for what you said, "If you are lucky, you may just touch it", as you have said, if you are lucky, no matter whether you are lucky or not, people ask for it.

"In a deck of playing cards (no ghosts), how many cards must be drawn at least to ensure that four cards are of the same suit", as mentioned above, that is to say, when drawing multiple cards, you must draw four cards of the same suit.