out of a set of 12 lights, 3 are burned out.

you have a set of 12 light switches in front of you numbered 1-12, with the 12 lights behind a glass wall.

each light switch will toggle the state of 2 lights.

the 2 lights it toggles will be 2*n %13, and 3*n %13.

for example, light switch 7 will toggle light 1, and light 8.

is it possible that: no matter what three lights are burned out, you can light up the remaining 9 lights?

Edited April 4, 201213 yr by phillip1882

I suspect that this hasn't been interpreted by the forum software in the way you expected.

the 3 lights it toggles will be 1*n %13, 2*n %13, and 3*n %13.

I guess the question should be

"Switch n will toggle 3 lights - (1*n) mod 13, (2*n) mod 13, (3*n) mod 13"

bah you guys are too quick. i modified the original question because i quickly realized it was too easy.

Surely if you throw all the switches then all the lights will be toggled three times ( ie on, off again, back on).

 

With mod 13 you will get 1 through 12 with the n*1 (in order), you will also get 1-12 with n*2 (going up by 2 each time) and also with n*3 (going up by 3)