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June 2000

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Brain-teaser - June 2001

In a factory workshop there are 13 lights, A,B,C,...L and M. At the end of the afternoon shift the supervisor has to inspect the shop floor to ensure that all is in order before locking up. To save him having to throw all thirteen switches, he has had 34 pairs of lights connected. They are AB, AC, AD, AJ, BC, BE, BI, CE, CF, CG, CH, CI, CK, CM, DE, DF, DG, DI, DJ, DK, DL, DM, EF, EG, EH, EI, EJ, EL, FJ, FM, GH, GM, KL and LM. Whenever a switch is thrown it changes the state of its own light and each of the lights connected to it from on to off or from off to on. For example, if switch A is thrown  then lights A, B, C, D and J go off. If next switch J is thrown then lights A, D and J are switched back on and lights E and F go off. At the end of the shift all the lights are on. Which switches should the supervisor throw to turn off all the lights.

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