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In decision problem versions of the art gallery problem, one is given as input both a polygon and a number k, and must determine whether the polygon can be guarded with k or fewer guards. This problem is -complete, as is the version where the guards are restricted to the edges of the polygon. [10]
An example water jar puzzle. The water jar test, first described in Abraham S. Luchins' 1942 classic experiment, [1] is a commonly cited example of an Einstellung situation. . The experiment's participants were given the following problem: there are 3 water jars, each with the capacity to hold a different, fixed amount of water; the subject must figure out how to measure a certain amount of ...
Archimedes's cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. Attributed to Archimedes , the problem involves computing the number of cattle in a herd of the sun god from a given set of restrictions.
A solution to Kirkman's schoolgirl problem with vertices denoting girls and colours denoting days of the week [1] Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary (pg.48). The problem states:
First, you have to understand the problem. [2] After understanding, make a plan. [3] Carry out the plan. [4] Look back on your work. [5] How could it be better? If this technique fails, Pólya advises: [6] "If you cannot solve the proposed problem, try to solve first some related problem. Could you imagine a more accessible related problem?"
The goat problems do not yield any new mathematical insights; rather they are primarily exercises in how to artfully deconstruct problems in order to facilitate solution. Three-dimensional analogues and planar boundary/area problems on other shapes, including the obvious rectangular barn and/or field, have been proposed and solved. [ 1 ]
The short-needle problem can also be solved without any integration, in a way that explains the formula for p from the geometric fact that a circle of diameter t will cross the distance t strips always (i.e. with probability 1) in exactly two spots. This solution was given by Joseph-Émile Barbier in 1860 [5] and is also referred to as "Buffon ...
A key concept in epistemic logic, this problem highlights the importance of common knowledge. Some authors also refer to this as the Two Generals' Paradox, the Two Armies Problem, or the Coordinated Attack Problem. [1] [2] The Two Generals' Problem was the first computer communication problem to be proven to be unsolvable. [3]