Need help with configuration of a touch sensing lamp project!
Seems too simple for a graduate EE project, but I guess this is the wrong field (no pun intended) , but you would learn about ESD protection and impedance ratios vs f with stray interference.
If you just use line frequency to detect lamp on, you will find lots of stray line interference, and less reliable with lack of ground specs.
If you model each person holding hands as 100pF for a fingertip and 1nF //&lt; 1 Meg then scale x N in series , choose a frequency and filter that will notch very high line E-fields (&gt;100Vac say) and very low signal current with BPF with 4kV ESD protection to detect current  of 50uA at sufficiently low impedance with your model but high Z for RF, AM etc. Work out the right f at Z(f) with specs 1st and the right amount of hysteresis.
An RLC Frequency Nomograph will help visualize the Impedances needed but using RC Active filters.  There are many free tools for doing Bode Filter Design plots. TI, Falstad afilter site, or your favourite software. The best tool is the one you learn how to use.