Required Mathematical Intelligence

Chapter 41 Finding the best strategy

There is a 100-story building, and you have two identical glass Go pieces in your hand.If you drop a Go piece from a certain floor of this building, it will break. Use the two glass Go pieces in your hand to find an optimal strategy to know the critical level.

[Answer: If there is only one chess piece in the hand, it must be thrown up from the second floor to the 2th floor. Now that there are two chess pieces in the hand, we can use the "life" of one of them in exchange for our faster acquisition of the critical layer .The basic idea is to divide the 100-story building into sections, first find the critical section, and then test layer by layer in the critical section to find the zero boundary layer.Similarly, we need to find the critical section from the lower level to the higher level, otherwise the sacrifice of the first chess piece may not let us know where the critical section is.Because we need to test one more time every time we go up to a critical section, and then we need to test the floors in the critical section.In order to ensure the optimization of the test, that is, the number of tests we need will not be too many under any circumstances, we should ensure that:

Number of times to find the zero boundary segment Find the critical layer

Try to equalize as much as possible, so our last critical section should be 1 less than the next critical section.
Since 1 2 3 ... 13 14=105, there are 5 more layers, which means that complete homogenization cannot be achieved. We can "digest" these 5 layers into some segments, and the purpose is to keep the balance as much as possible.We can think that the bottom section is 14 layers (or 13 layers, assuming that one of the layers is "digested" in the first section), and start the test from this. If it is not broken, go up a section, and if it is broken, go from bottom to top in this layer. Keep testing.

The idea is that no matter where the critical layer is, the number of times we need to find it should not be many. ]
(End of this chapter)