The first is the elaboration of the ladder game ... The game is on a ladder ... The natural number of points is placed on each ladder. Two people to play ladder game ... Each step is to move a number of points (>=1) from one group to the front. Finally, there is no point to move the person to lose.
As this is the initial state of a ladder Game 2 1 3 2 4 ... You can only put the back point on the front side. How to analyze This problem ... In fact, the ladder game can be transformed into NIM. Think of all the odd steps as n heap stones. Do Nim. Moving stones from odd piles to even heaps can be understood as taking away stones. It's the equivalent of a few odd piles of pebbles doing NIM. (as given in the example: 2^3^4=5 is not zero so the initiator will be defeated. Suppose we are the initiator ... Given the ladder of gravel state of odd piles to do nim can win ... I'm going to follow the winning steps to move the odd heap of pebbles to even heaps ... If the opponent is also moving odd heaps. We continue to move odd piles. If the opponent moves an even heap of pebbles to an odd heap. Then we move so many of the stones that the opponent moved from that odd pile to the even heap below ... After two operations ... The equivalent of even heaps of gravel moved down several. And the odd pile still looks the same ... That is the state of winning ... Even though the flip-out has been moving even heaps of pebbles into odd piles. We've been following him. Keep the stones moving down. Keep odd heaps constant ... To do so. I can follow my hand to move even piles of stones to 0. Then you can't move the stones ... So the whole process. Moving an even heap to an odd heap does not affect the odd heap of the Nim game process. The whole process can be abstracted as an odd heap of Nim games ... The other situation ... The initiator must lose ... Similar reasoning ... Just judge the odd heap to do nim game situation can ... Why is only the odd pile of Nim can ... Instead of even heaps? ... Because if it's a dual heap of Nim ... The opponent moves the odd heap of pebbles to even heaps. Let's move these stones to the next odd pile ... Then finally the opponent moved the stones to 0. We can't keep moving ... can only destroy the original Nim and lead to the uncertainty of the relationship between the outcome ... So as long as the odd heap to do NIM judgment can know the outcome of the situation ...
"Reprint" Ladder Game
