预言纸牌的魔术，为什么常常用到模运算？
Why do card-prediction tricks often use modular arithmetic?
把牌面映射成数字后，移牌、切牌等操作等价于在模某个数下做加减。魔术师用同余关系算出牌堆中某张固定位置的牌，从而看似预言。
Mapping cards to numbers turns cuts and deals into addition or subtraction modulo n. The magician uses congruences to track a card at a fixed position, seemingly predicting it.
难度 专业 · 适合 初中(12-15)
CC BY 4.0 · 已核验 · Verified 2026-10-03
来源 · Source
《什么是数学》(柯朗)（数论章：同余）
What Is Mathematics? (Courant), chapter on number theory (congruence)
#数学魔术 #模运算
扑克牌魔术里四张A怎么会凭空多出来？
In a card trick, how can four aces seem to multiply?
这类魔术多用强迫选牌、预先叠放和错位收牌等手法，配合观众注意力的转移。数学上靠排列组合的确定性，而非真的变出牌。
Such tricks rely on force selections, pre-stacked orders and false shuffles plus misdirection. Mathematically they use the determinism of permutations, not real multiplication of cards.
难度 进阶 · 适合 大众
CC BY 4.0 · 来源待核验 · Source pending review
来源 · Source
出处备注：本题原挂出处与答案内容不符，已撤回；具体书目待补，暂不展示来源。
本题原挂出处与答案内容不符，已撤回；具体书目待补。
Previous citation withdrawn as unsupported for this answer; a specific source is pending.
#数学魔术 #排列
一个读心小魔术：想个三位数，把它重复成六位数，为什么一定能被7、11、13整除？
Magic trick: think of a 3-digit number, repeat it to make a 6-digit number, why is it always divisible by 7, 11 and 13?
把abc写成abcabc，等于abc×1001，而1001=7×11×13。所以无论想什么三位数，重复后都能被这三个数整除，魔术师据此猜出原数。
Writing abc as abcabc equals abc×1001, and 1001=7×11×13. So whatever 3-digit number you pick, the repeat is divisible by all three, letting the magician recover it.
难度 入门 · 适合 大众
CC BY 4.0 · 已核验 · Verified 2026-08-23 · 2 条独立证据
来源 · Source
Martin Gardner,《My Best Mathematical and Logic Puzzles》Dover,1994
M. Gardner, My Best Mathematical and Logic Puzzles, Dover, 1994
独立核验依据 · Independent verification: 核验依据 2 OPENLIBRARY 标识 /works/OL460047W：My best mathematical and
#数学魔术 #整除