Problem 7, Combinatorics

I proposed this problem in the last mathematical competition hosted on the Italian ‘gasmatematica’ website. The numbers from 000 to 999 must be put into some boxes, numbered from 00 to 99. If the label of a box is equal to a number with one digit removed, then the number can be put in that […]

A Problem From Stanford Mathematics Tournament 2008 (Team Test)

Daphne is in a maze of tunnels shown below. She enters at A, and at each intersection, chooses a direction randomly (including possibly turning around). Once Daphne reaches an exit, she will not return into the tunnels. What is the probability that she will exit at A? The Idea At first, I will denote by […]

A Very Notorious Problem, But In 3D

I’ve already made an article on the 2D version of this problem, if you want to check it out before this one, you can visit Now, the 3D version says: if you have 3 reals x, y, z chosen randomly between 0 and 1, what’s the probability that It’s important to notice that any […]

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