Cunning Combination Problems & Other Puzzles

There's magic in these brainteasers. Most of them play variations on the magic square, among the oldest puzzles that exist. These cubes or other shapes are made up of groups of cells, each cell containing one of a set of numbers. The set generally corresponds with the number of cells, so, for example, a five-by-five magic square would contain numbers from 1 to 25. The the sum of the numbers in any one row or column (and sometimes diagonal) must be the same. It's pure mathematical beauty. Examine and attempt to figure out the workings of a "diabolic" version created by Dürer, an early variation by Lo-Shu, and variants that use colors, different shapes, and hinged tiles.