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.