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The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations.
Martin Gardner presents and discusses the problem [1] in his book of mathematical puzzles published in 1979 and cites references to it as early as 1895. The crossed ladders problem may appear in various forms, with variations in name, using various lengths and heights, or requesting unusual solutions such as cases where all values are integers.
The Tower of Hanoi (also called The problem of Benares Temple, [1] Tower of Brahma or Lucas' Tower, [2] and sometimes pluralized as Towers, or simply pyramid puzzle [3]) is a mathematical game or puzzle consisting of three rods and a number of disks of various diameters, which can slide onto any rod.
A magic triangle or perimeter magic triangle [1] is an arrangement of the integers from 1 to n on the sides of a triangle with the same number of integers on each side, called the order of the triangle, so that the sum of integers on each side is a constant, the magic sum of the triangle.
A direct proof using classical geometry was developed by James Mercer in 1923. [2] This solution involves drawing one additional line, and then making repeated use of the fact that the internal angles of a triangle add up to 180° to prove that several triangles drawn within the large triangle are all isosceles.
The Erdős–Oler conjecture: when is a triangular number, packing circles in an equilateral triangle requires a triangle of the same size as packing circles. [ 47 ] The disk covering problem abount finding the smallest real number r ( n ) {\displaystyle r(n)} such that n {\displaystyle n} disks of radius r ( n ) {\displaystyle r(n)} can be ...
The Penrose triangle, also known as the Penrose tribar, the impossible tribar, [1] or the impossible triangle, [2] is a triangular impossible object, an optical illusion consisting of an object which can be depicted in a perspective drawing.
Another way to change the puzzle is to restrict which colors squared make up the border colors. In the classic MacMahon squares puzzle, there are a total of 20 places on the border. [1] The number of each color that can be present on these 20 places can be described by B a,b,c [1] where a, b, and c are the number of each color of the border pieces.