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The question of minimizing the number of crossings in drawings of complete bipartite graphs is known as Turán's brick factory problem, and for , the minimum number of crossings is one. K 3 , 3 {\displaystyle K_{3,3}} is a graph with six vertices and nine edges, often referred to as the utility graph in reference to the problem. [ 1 ]
To obtain 4 liters using 3-liter and 5-liter jugs, we want to reach the point (4, 0). From the point (4, 0), there are only two reversible actions: filling the empty 3-liter jug to full from the tap (4,3), or transferring 1 liter of water from the 5-liter jug to the 3-liter jug (1,3). Therefore, there are only two solutions to the problem:
Predict what the water level in units will be on the left side. Typical Solutions. Someone with knowledge about the area of triangles might reason: "Initially the area of the water forming the triangle is 12 since 1 / 2 × 4 × 6 = 12. The amount of water doesn't change so the area won't change. So the answer is 3 because 1 / 2 ...
The potato paradox is a mathematical calculation that has a counter-intuitive result.The Universal Book of Mathematics states the problem as such: [1]. Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water (being purely mathematical water).
A cup of wine is taken from the wine barrel and added to the water. A cup of the wine/water mixture is then returned to the wine barrel, so that the volumes in the barrels are again equal. The question is then posed—which of the two mixtures is purer? [1] The answer is that the mixtures will be of equal purity.
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
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[1] 1. Cantor's problem of the cardinal number of the continuum. 2. The compatibility of the arithmetical axioms. 3. The equality of the volumes of two tetrahedra of equal bases and equal altitudes. 4. Problem of the straight line as the shortest distance between two points. 5.