The 50 bulbs problem

Prime Minister of Einsteinia lost the Mensa annual challenge and committed suicide.The King of Einsteinia had some doubts on the abilities of the Deputy Prime Minister. The King devised a plan to test his intelligence before promoting him.

He put 50 light bulbs in a room and put the corresponding 50 switches in another room. He switched on "x" number of these bulbs. He told the Deputy Prime Minister the number of bulbs that are switched on (x) and gave him the task of dividing the fifty switches into two groups such that each group had equal number of lit bulbs. The Deputy Prime Minister was allowed to go to the room with the bulbs or to the room with the switches but could not see one room from the other. By looking at the switch there is no way to tell whether the corresponding bulb is on or off. Flipping the switch each time toggles the state of the corresponding bulb.

Can you help the Deputy Prime Minister in devising a strategy?


Solution:
Ba cbfvgvba - Gur ohyo gb juvpu gur fjvgpu orybatf gb vf BA (abg gur culfvpny cbfvgvba bs gur fjvgpu)

Yrgf fnl gur QCZ pubbfrf nal 'k' fjvgpurf bhg bs gur 50.
Abj, vs 'a' fjvgpurf bhg bs guvf 'k' ner va gur BA cbfvgvba gur erfg bs gur 'k-a' fjvgpurf juvpu ner nyfb BA orybat gb gur bgure tebhc bs '50 - k' fjvgpurf.

Fb, abj vs gur QCZ gbttyrf gur cbfvgvba bs nyy gur 'k' fjvgpurf gung ur fryrpgrq, 'a-k' fjvgpurf jbhyq abj or va gur BA cbfvgvba. Guvf vf fnzr nf gur ahzore bs fjvgpurf va gur BA cbfvgvba va gur bgure tebhc.

use rot13