No subject

is
             56, which translates into 64 ICMP data bytes when combined
with
             the 8 bytes of ICMP header data.
(apologies for ugly formatting)

hobbes:~$ ping 10.1.1.20
PING 10.1.1.20 (10.1.1.20): 56 data bytes
64 bytes from 10.1.1.20: icmp_seq=0 ttl=255 time=0.3 ms
64 bytes from 10.1.1.20: icmp_seq=1 ttl=255 time=0.2 ms

hobbes:~$ ping -s 56 10.1.1.20
ping: Operation not permitted
hobbes:~$ ping -s 1000 10.1.1.20
ping: Operation not permitted

hobbes:~# ping -s 56 10.1.1.20
PING 10.1.1.20 (10.1.1.20): 56 data bytes
64 bytes from 10.1.1.20: icmp_seq=0 ttl=255 time=0.3 ms

hobbes:~# ping -s 1000 10.1.1.20
PING 10.1.1.20 (10.1.1.20): 1000 data bytes
1008 bytes from 10.1.1.20: icmp_seq=0 ttl=255 time=0.8 ms


Am I missing something?  Perhaps your users were ping flooding some other
way in which case it would be interesting to find out how...

Regards,

Christian.