初级Beginner点子Idea
管道里有噪音：我知道你翻了哪一张
A Noisy Pipe: I Know Which Card You Flipped
翻一张卡，老师回头一眼就找出来。多加一行一列“校验位”，错误能被发现，还能改回来。
Flip one card and the teacher finds it at a glance. One extra row and column of check bits can find a mistake and fix it.
这是一个课程点子：活动和资料都有，学习单还没做。
This is a lesson idea: the activities and links are ready, the worksheets are not made yet.
管道有时会“串线”：你发的 1，到了对面变成了 0。对方怎么知道传错了？能不能自己改回来？
Sometimes the pipe gets noisy: you send a 1 and it arrives as a 0. How can your friend tell? Can they fix it?
孩子做什么What kids do
- 魔术：学生用 25 张双面卡随意摆成 5 × 5，老师“顺手”再加一行一列。老师转身，学生翻一张，老师回头一眼找出来。Magic trick: a student lays out 25 two-sided cards in a 5 × 5 square, and the teacher “casually” adds one more row and column. The teacher turns away, a student flips one card, and the teacher finds it at a glance.
- 揭秘：老师加的那一行一列有什么规律？（每行每列的黑卡都是偶数张）The secret: what is special about the extra row and column? (Every row and column has an even number of black cards.)
- 换学生当魔术师。再试试：翻两张，还能发现吗？Now a student is the magician. Try flipping two cards: can you still tell?
要点Key idea
多加的那几张叫“校验位”（奇偶校验）。出错的那一行和那一列交叉的地方，就是出错的位置，所以不但能发现错误，还能改回来。
The extra cards are check bits (parity). The wrong row and the wrong column cross at the mistake, so you can find it and fix it.
和 AI 的关系Where AI comes in
二维码缺一角还能扫、信号不好时照片也不会花、太空探测器从很远的地方传回照片，靠的都是“多发一点点”。
A QR code with a corner missing still scans, a photo still arrives clean on a weak signal, and space probes send pictures home from far away, all by sending a little extra.
视频与文章Videos and reading
- CS Unplugged: Mind-reading magic 魔术步骤和视频steps and video
- Computer Science Buskers? (Error Detection) 5 分钟，街头表演这个魔术5 min, the trick as a street show
- CS Field Guide: The parity magic trick 原理how it works
- 3Blue1Brown: But what are Hamming codes? 20 分钟，大孩子和老师20 min, older kids and teachers