/leyuan.htm

Choose a very interesting math problem for primary school students, and fifth-grade students should be able to understand it, hehe ~

Reverse transformation, skillfully take coins.

Cha zhigang

Ever heard of coin games? If you haven't heard of it, get familiar with the rules of the coin game first! The coin withdrawal game is a game played by two people. Each participant is required to take several coins in turn, and whoever gets the last coin wins. Let's play a game of taking coins.

Game 1: There are 15 coins on the table, and two players (you and one of your classmates) take several coins in turn. The rule is that each person takes at least 1 coin and at most 5 coins at a time. Whoever gets the last one will win all 15 coins.

The game has started, and you must be thinking: Is there any way to ensure that you win? If so, what is the method? Now imagine yourself in a winning state. It's your turn to take coins. There are no more than five coins on the table. At this time, you can take all the coins on the table at once and become the winner. Now, can you move forward from this final state and find a state so that as long as your opponent is in this state, no matter how many coins he takes, you will be in an ideal winning state? It is not difficult to find that if your opponent has six coins on his desk, no matter how much he takes (from 1 to 5), there will be at least 1 and at most five coins left on the desk, so the victory must belong to you. In other words, whoever takes the ninth coin (15-6 =) wins. Therefore, the winning situation of the game 1 is the same as that of the next game 2.

Game 2: There are 9 coins on the table. Two players (you and one of your classmates) take turns to take a few coins. The rule is that each person takes at least 1 block and at most 5 pieces, and whoever gets the last piece wins 15 coins.

From the backward analysis of the first 1 game, we can easily know that the outcome of the second game is the same as that of the third game.

Game 3: There are three coins on the table. Two players (you and one of your classmates) take some in turn. The rule is that each person takes at least 1 block and at most 5 pieces, and whoever gets the last piece wins 15 coins.

In the third game, you only need to be the first to take three coins from the table to win. It can be seen that if you want to win the game of 1, as long as you take the three coins on the table first, you will definitely win.

Think about it: play the following game with your children by using the best strategy above: put 30 coins on the table, and two players (you and one of your classmates) take several in turn. The rule is that everyone takes at least two coins at a time and at most six coins, and whoever gets the last one wins all 30 coins.