There are n binary levers: each lever can be in position 0 or position 1.
Exactly one out of 2^{n} possible combinations of levers opens the lock.
The lock opens immediately as soon as each lever is in proper position.
Changing position of one lever is called a move.
Suppose all levers are initially in position 0.
What is the minimal number of moves that guarantees opening the lock?
In other words: how many moves are required to test each position of levers (the worst case scenario)?

Can you also describe the optimal procedure of moving the levers?

Posted

There are n binary levers: each lever can be in position

0or position1.Exactly one out of 2

^{n}possible combinations of levers opens the lock.The lock opens immediately as soon as each lever is in proper position.

Changing position of one lever is called a

move.Suppose all levers are initially in position

0.What is the minimal number of moves that guarantees opening the lock?

In other words: how many moves are required to test each position of levers (the worst case scenario)?

Can you also describe the optimal procedure of moving the levers?

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