# 3 switches and 4 lights

The are three switches (1, 2 and 3) and four lights (A, B, C and D). Each switch turns on exactly two lights and no two switches turn on identical lights. You know that

• Lights A, B and C are on when switches 1 and 2 are down.
• Lights A, C and D are on when switches 1 and 3 are down.
• Lights B, C and D are on when switches 2 and 3 are down.

Can you figure out which switch controls which lights? Good luck!

• 3 - A & B, 2 - A & D, 1 - B & D. Sep 26, 2020 at 11:14
• Unmentioned lights are off? Without that rule, there are 7 solutions instead of 1. Sep 26, 2020 at 16:14
• yes they are off Sep 27, 2020 at 0:09

1 is A and C because if 1 is D then 1 and 2 would have D, if one was B then 1 and 3 would have B.

2 is B and C because if it was A then 2 and 3 would have A if D then 1 and 2 would have D.

3 is C and D because if B then 1 and 3 would have b and if A then 2 and 3 would have A.

C is forever on.

-------------------------
|  A  |  B  |  C  |  D  |
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|  +  |  +  |  *  |     |    3rd lamp is on
-------------------------
|  +  |     |  *  |  +  |    2nd lamp is on
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|     |  +  |  *  |  +  |    1st lamp is on
-------------------------


So, 3 - A & B, 2 - A & D, 1 - B & D

PS: I don't know how to hide all these things. What I know is >! and that hides only one block of sentence or paragraph.