# Search results

1. ### Modified Huffman Encoding

Problem: A telegraph machine can transmit only lines and dots; it takes 2 seconds to transmit a line, but only 1 second to transmit a dot. We generally want to transmit texts containing letters of the English alphabet, and digits (so we have N<=36 symbols in total). Therefore, a prefix-free...
2. ### Pairwise Product Set Cardinality

Source: Nick's Mathematical Puzzles Problem:Let n be a positive integer, and let $$S_n = {n^2 + 1, n^2 + 2, ... , (n + 1)^2}$$. Find, in terms of n, the cardinality of the set of pairwise products of distinct elements of $$S_n$$ For example, $$S_2 = {5, 6, 7, 8, 9},$$ 5 × 6 = 6 × 5 = 30, 5 × 7...
3. ### Veit Elser’s Formidable 14

This is another of those problems I have not been able to solve since over an year. Fit disks of the following diameters into a circular cavity of size 12.000: 2.150 2.250 2.308 2.348 2.586 2.684 2.684 2.964 2.986 3.194 3.320 3.414 3.670 3.736 Write a program or give a general algorithm to...
4. ### Russian Roulette (Difficult Version)

I got this problem from Peter Winkler's Puzzle Book. I have not been able to solve it since 2 years now. In a room stand n armed and angry people. At each chime of a clock, everyone simultaneously spins around and shoots a random other person. The persons shot fall dead and the survivors spin...