# Pairing up Socks

On a nice day, Babai, a computer scientist, received back all 6 pairs of my $$\color{blue}{blue}$$ and $$\color{red}{red}$$ socks in a laundry basket. He needed to pair them up into pairs of same color for me.

Being a computer scientist, he wondered what would be a good way to sort them out. Can you help him by figuring out the faster way to sort these?

Swap and Go:

1. Lay the socks on the table side by side.
2. While there are some $$\color{blue}{blue}$$ socks in the last 6 socks, do the following:
• Going from left to right, if there is a $$\color{red}{red}$$ sock to the right of a $$\color{blue}{blue}$$ sock, exchange them.
3. Now, all 6 pairs of adjacent socks are each of the same color. So, take two at a time and pair them up.

Throw into Buckets:

1. Lay the socks on the table side by side. Take two buckets, $$\color{red}{red}$$ and $$\color{blue}{blue}$$.
2. For all the socks on the table, check which of them are $$\color{red}{red}$$, one by one:
• if a sock is $$\color{red}{red}$$, put it in the $$\color{red}{red}$$ bucket;
• if a sock is $$\color{blue}{blue}$$, put it in the $$\color{blue}{blue}$$ bucket.
3. Now, we know that all the $$\color{red}{red}$$ and $$\color{blue}{blue}$$ socks are each in the bucket of the same color. Taking two of them at a time from the same bucket, pair them up.
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