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The most classic game of two people taking turns to take beads

2024-10-20 06:07
2024-10-20 07:06

In a game where two people took turns to pick up beads, there were a total of 40 beads. Starting from the first bead, they could pick up a maximum of four beads at a time, and a minimum of one bead at a time. They had to pick up the last bead. Whoever picked up the last bead would win. First, we can consider an optimal strategy. Assuming that the first player needed to get the $n$bead to win, then the second player only needed to get the $n-1 $bead, the $n-2$bead, the $n-3$bead, the $n-4$bead, the $n-5$bead, the $n-6$bead, the $n-7$bead, the $n-8$bead, the $n-9$bead, the $n-10 $bead, the $n-11 $bead, the $n-12 $bead. No.$n-13 $, No.$n-14 $, No.$n-15 $, No.$n-16 $, No.$n-17 $, No.$n-18 $, No.$n-19 $, No.$n-20$, No.$n-21$, No.$n-22$, No.$n-23$, No.$n-24$, No.$n-25$, No.$n-26$No.$n-27$, No.$n-28$, No.$n-29$, No.$n-30$, No.$n-31$, No.$n-32$, No.$n-33$, No.$n-34$, No.$n-35$, No.$n-36$, No.$n-37$, No.$n-38$, No.$n-39$, No.$n-40$, It would guarantee the victory of the player who came after him. Therefore, the first player needed to adopt the optimal strategy. The number of beads taken each time and the number of beads taken by the second player was 5. This way, the first player could guarantee that he would get the 40th bead and win. While waiting for the TV series, you can also click on the link below to read the classic original work of "Dafeng Nightwatchman"!

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