How to broadcast ping

I've been trying to find all of the laptops on my college's wireless network to see if i can find my friend's laptop, who is sitting right across from me. I checked google's results for broadcast ping, and found that if you take the default IP address, and the subnet mask, and add 255 to the last part of the IP, it should ping all devices capable of responding to a ping. My problem is that my college's IP address and subnet mask are different from all of the examples i've seen online. The default IP is 10.223.0.1, and the subnet mask is 255.255.252.0. However, i have noticed that the router assigns not only the last part of the IP to a device, but the second to last as well, so MY IP address is 10.223.3.136. Whenever i try pinging 10.223.0.255, i just keep getting timeouts. When i change it to 10.223.3.255, then i get a response from my own computer, but when i do the same with his, i get timeouts as well. Any ideas on how to get this to work?