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The solution to this particular problem is given by the binomial coefficient (+), which is the number of subsets of size k − 1 that can be formed from a set of size n + k − 1. If, for example, there are two balls and three bins, then the number of ways of placing the balls is ( 2 + 3 − 1 3 − 1 ) = ( 4 2 ) = 6 {\displaystyle {\tbinom {2 ...
Three utilities problem – Connect three cottages to gas, water, and electricity without crossing lines. [ 9 ] Thirty-six officers problem – Arrange six regiments consisting of six officers each of different ranks in a 6 × 6 square so that no rank or regiment is repeated in any row or column.
One solution of the nine dots puzzle. It is possible to mark off the nine dots in four lines. [13] To do so, one goes outside the confines of the square area defined by the nine dots themselves. The phrase thinking outside the box, used by management consultants in the 1970s and 1980s, is a restatement of the solution strategy. According to ...
In the field of computer science, the method is called generate and test (brute force). In elementary algebra, when solving equations, it is called guess and check. [citation needed] This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory.
The Torrance Tests of Creative Thinking, formerly the Minnesota Tests of Creative Thinking, is a test of creativity built on J. P. Guilford's work and created by Ellis Paul Torrance, the Torrance Tests of Creative Thinking originally involved simple tests of divergent thinking and other problem-solving skills, which were scored on four scales:
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields.
One strategy for solving this version of the hat problem employs Hamming codes, which are commonly used to detect and correct errors in data transmission. The probability for winning will be much higher than 50%, depending on the number of players in the puzzle configuration: for example, a winning probability of 87.5% for 7 players.
Although the three-peg version has a simple recursive solution long been known, the optimal solution for the Tower of Hanoi problem with four pegs (called Reve's puzzle) was not verified until 2014, by Bousch. [20] However, in case of four or more pegs, the Frame–Stewart algorithm is known without proof of optimality since 1941. [21]