Boolean Expression Solver is a commandline utility that generates a truth table for a given Boolean expression. It is written in Java, so it will run on any platform that has the Java runtime environment installed, but the makefile and shell-script included for convenience generally require *nix.
SyWiCo is a tool for managing concurrent modifications of shared files between unconnected computers. It can be used as a synchronization tool relying on email. Its main design goal was for synchronizing the source code by email between developers, when the use of a source control software is not possible. The communication is stateless and reduced to a very small number of messages, typically 2 or 4. It does not create any files in the directories that it synchronizes, and leaves one participant free from dealing with merging and conflict resolution. This is not a tool to replace source control programs, as it provides no versioning.
Lanshark is a file sharing tool for local area networks. It allows you to share files with other users in the same network more efficiently. It automatically detects other lanshark users in the same network and lets you browse through their shares. It has a very fast search function that allows you to search through all the shares in the network in a few seconds.
net-status-monitor is a simple console script to test whether Internet connectivity is working. If it is, the script tells you the external IP address (in case your dynamic DNS provider is down). If not, it tries to find the point where the connectivity fails. The output is quite simple, so you can put it on your grandmother's PC. "Just tell me what the read line says" should give you enough information.