Raj installed 2000 bulbs in a company with the condition that only one bulb will light up at a single time. What
will be the minimum amount of switches to be installed such that using their combination it will be possible to
light up any bulb. Considering that it is possible to set a bulb such that it will light up only in a unique set of
switches combination
Answers
Given : Raj installed 2000 bulbs in a company with the condition that only one bulb will light up at a single time. it is possible to set a bulb such that it will light up only in a unique set of switches combination
To Find : What will be the minimum amount of switches to be installed such that using their combination it will be possible to
light up any bulb.
Solution
Each Switch has two positions
Let say there are n switches
total possible arrangement will be
2 * 2 * 2 * ................................* 2 ( n times)
= 2ⁿ
2000 bulbs
=> 2ⁿ > 2000
2048 > 2000 > 1024
=> 2¹¹ > 2000 > 2¹⁰
=> 2¹¹ > 2000
2ⁿ > 2000
=> n = 11
11 is the minimum amount of switches to be installed such that using their combination it will be possible to light up any bulb
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