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一些有趣的数学、物理、计算机问题 ...

问题： 想象光滑的地面有两个静止的小滑块，左面有一堵质量无穷大的墙。左边的小滑块质量为 $1$。此时给右边的小滑块一个向左的速度，假设所有的碰撞...

Finding the best route between two cities, given a complicated road network; or transmitting a message between two computers along a network of hundreds of computers, are all classified as the shortest path problem. ...

Given $n$ workers and $n$ jobs, and the cost $c_{ij}$ to train the $i$-th worker for the $j$-th job, find an assignment of one worker to each job which minimized the total training cost. ...

Find the smallest integer $n$ that there must be either three mutual friends or three mutual strangers among $n$ people, suppose each pair of people are either friends or strangers? ...

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects. ...

Various ways of distributing balls into cells. ...

It is extremely difficult, and often impossible, to prevent errors when data are stored, retrieved, operated on, or transmitted. ...

Any mathematical system containing all the theorems of arithmetic is an incomplete system. ...

问题： 证明 $1+\dfrac{1}{4}+\dfrac{1}{9}+\dfrac{1}{16}+\cdots=\dfrac{\pi^2}{6}$ 这一问题实际上有多种代数方法证明，但由于公式中出现了 $\pi$ ，则必定在几何学中可以找到圆来对应。 想象一位观察者站在数轴的原点，并在所有...