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Eight light bulbs are placed on the eight lattice points (±1,±1,±1). Each light bulb can either be turned on or off. However, the lightbulbs are unstable, and if two light bulbs with distance less than or equal to 2 are on simultaneously, both lights explode. How many possible configurations of on/off light bulbs exist if no explosions occur?

Eight light bulbs are placed on the eight lattice points (±1,±1,±1). Each light bulb can either be turned on or off. However, the lightbulbs are unstable, and if two light bulbs with distance less than or equal to 2 are on simultaneously, both lights explode. How many possible configurations of on/off light bulbs exist if no explosions occur?

Grade:11

1 Answers

jitender lakhanpal
62 Points
7 years ago

hi vivek 

 

quite an easy question 

there are 8 bulbs in 8 quadrants the coordinates are 

first qudrant   bulb B1 = (1,1,1)

second quadrant  B2 = ( 1,-1,1 )  AND SO ON IT FORMS A CUBE  OF 2 UNITS 

SO ALL THE BULBS IN THE DIAGONAL WILL NOT EXPLODE 

THE DISTANCE BETWEEN THE FACE DIAGONAL AND BODY DIAGONAL WILL BE GREATER THAN 2 

2 ROOT 2 AND 2 ROOT 3 RESPECTIVELY  SO ALL THE POSSIBLE CONFIGURATION YOU CAN EASILY FIND OUT

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