witzar

There are n binary levers: each lever can be in position 0 or position 1. Exactly one out of 2n 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?

Edit:

Well done, gavinksong.

This puzzle is inspired by posted by bonanova. Again we work on a hexagonal tiling of a plane, and the question is about possibility of covering some shape with triminoes. Trimino is a "triangle" formed by three unit hexagons sharing common vertex. The shape to cover is defined as follows: Let's pick a unit hexagon and call it H1. Now we recursively define Hn+1 as a sum of Hn and all unit hexagons adjacent to Hn. So basically Hn is a "hexagon" with side of length n (unit hexagons). Let Dn be Hn with one unit hexagon at it's center removed. So, can you cover D2015 with triminoes?