0
votes
1answer
23 views

Understanding a complex set description

I am trying to understand the following math expression, describing the possible sets of a 15 Puzzle: The expressions for tile and ...
0
votes
1answer
77 views

Exponent Upon Exponent? [duplicate]

I can't understand this. Can you please make a clearer explanation?
8
votes
2answers
350 views

Explain a surprisingly simple optimization result

The following optimization problem came to my attention as an idealization of the silly browser game Cookie Clicker, but is representative of a range of strategy games: You have an initial ...
1
vote
1answer
1k views

Pattern-matching puzzle (shapes)

some puzzle that can be found online are typically a 3x3 grid where you've got nine spots filled with some images or symbols or geometric figures and you have to predict what the missing one should ...
10
votes
4answers
1k views

Ten soldiers puzzle

This is a puzzle from one popular book called "The Man Who Counted: A Collection of Mathematical Adventures",author is Malba Tahan. How to arrange ten soldiers in five lines in such a way that each ...
13
votes
5answers
1k views

Four men, hats and probability

I encountered the four men in hats puzzle for the first time today. My question is about a realisation I (think I) had while arriving at the solution, but I have no idea whether I've made a mistake ...