孩子做什么What kids do

1. 先玩再想：两人一组，在学习单印好的硬币上用铅笔划掉来玩，擦掉再玩。Play first: in pairs, cross out the coins on the worksheet in pencil, erase, and play again.
2. 把问题变小：只剩 1、2、3 枚时轮到你，你会赢吗？4 枚呢？全班在白板上倒着推。Make it smaller: with 1, 2 or 3 coins left on your turn, do you win? With 4? The class works backward on the whiteboard.
3. 找规律：哪些数字轮到你，你就一定会输？Find the pattern: which numbers make you lose if it is your turn?
4. 变一变：拿到最后一枚的人输；或者一次可以拿 1–4 枚。Change the rules: whoever takes the last coin loses, or you may take 1 to 4 coins.
5. 自己出题：设计一个“后手必胜”的游戏，去考同学。Make your own: design a game the second player always wins, and test a classmate.
6. 火柴盒 AI：用纸杯和彩色珠子做一台会自己学会这个游戏的机器（1961 年的 MENACE）。Matchbox AI: build a machine of paper cups and colored beads that learns the game by itself (like MENACE, 1961).

要点Key idea

必输的数是 4 的倍数：对方拿几枚，你就拿几枚凑成 4。从最小的情况倒着推，叫倒推法，电脑下棋时做的也是这件事。

The losing numbers are multiples of 4: whatever the other player takes, you take enough to make 4. Working back from the smallest case is called backward induction, and a chess computer does the same thing.

和 AI 的关系Where AI comes in

表填得完就查表；填不完就往前看几步，再估一估。AlphaGo 自己和自己下棋，学会了估那张填不完的表。

If the win/lose table can be filled in, just look it up. If it can’t, look a few moves ahead and estimate. AlphaGo learned to estimate that endless table by playing against itself.

视频与文章Videos and reading

• MindYourDecisions: Can You Solve The 21 Flags Game From Survivor? 8 分钟，真人秀里的同一个游戏8 min, the same game on a TV show
• Vsauce2: A Game You Can Always Win 10 分钟，卡罗尔的“抢 100”10 min, Lewis Carroll’s race to 100
• NRICH: Got It 在教室电脑上和电脑对战play against the computer in class
• Beast Academy: Nim (printable) 给小朋友的讲解和练习explanation and practice for kids
• Stand-up Maths: MENACE, the pile of matchboxes which can learn 14 分钟，火柴盒 AI14 min, the matchbox AI
• Google DeepMind: AlphaGo – The Movie 90 分钟纪录片90 min documentary
• Wikipedia: Solved game 哪些游戏已经被“解开”which games have been solved

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