Shell script: Count files, delete 'X' oldest file - linux

Question

I am new to scripting. Currently I have a script that backs up a directory every day to a file server. It deletes the oldest file outside of 14 days. My issue is I need it to count the actual files and delete the 14th oldest one. When going by days, if the file server or host is down for a few days or longer, when back up it will delete a couple days worth of backups or even all of them. Pending down time. I want it to always have 14 days worth of backups.
I tried searching around and could only find solutions related to deleting by dates. Like what I have now.
Thank you for the help/advice!
My code I have, sorry its my first attempt at scripting:
#! /bin/sh
#Check for file. If not found, the connection to the file server is down!
if
[ -f /backup/connection ];
then
echo "File Server is connected!"
#Directory to be backed up.
backup_source="/var/www/html/moin-1.9.7"
#Backup directory.
backup_destination="/backup"
#Current date to name files.
date=`date '+%m%d%y'`
#naming the file.
filename="$date.tgz"
echo "Backing up directory"
#Creating the back up of the backup_source directory and placing it into the backup_destination directory.
tar -cvpzf $backup_destination/$filename $backup_source
echo "Backup Finished!"
#Search for folders older than '+X' days and delete them.
find /backup -type f -ctime +13 -exec rm -rf {} \;
else
echo "File Server is NOT connected! Date:`date '+%m-%d-%y'` Time:`date '+%H:%M:%S'`" > /user/Desktop/error/`date '+%m-%d-%y'`
fi

Answer 1

Something along the lines like this might work:
ls -1t /path/to/directory/ | head -n 14 | tail -n 1
in the ls command, -1 is to list just the filenames (nothing else), -t is to list them in chronological order (newest first). Piping through the head command takes just the first 14 from the output of the ls command, then tail -n 1 takes just the last from that list. This should give the the file that is 14th newest.

Answer 2

Here is another suggestion. The following script simply enumerates the backups. This eases the task of keeping track of the last n backups. If you need to know the actual creation date you can simply check the file metadata, e.g. using stat.
#!/bin/sh
set -e
backup_source='somedir'
backup_destination='backup'
retain=14
filename="backup-$retain.tgz"
check_fileserver() {
nc -z -w 5 file.server.net 80 2>/dev/null || exit 1
}
backup_advance() {
if [ -f "$backup_destination/$filename" ]; then
echo "removing $filename"
rm "$backup_destination/$filename"
fi
for i in $(seq $(($retain)) -1 2); do
file_to="backup-$i.tgz"
file_from="backup-$(($i - 1)).tgz"
if [ -f "$backup_destination/$file_from" ]; then
echo "moving $backup_destination/$file_from to $backup_destination/$file_to"
mv "$backup_destination/$file_from" "$backup_destination/$file_to"
fi
done
}
do_backup() {
tar czf "$backup_destination/backup-1.tgz" "$backup_source"
}
check_fileserver
backup_advance
do_backup
exit 0