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The simplest solution for 5 liters is (9,0) → (9,8) → (12,5); The simplest solution for 4 liters is (9,0) → (12,0) → (4,8). These solutions can be visualized by red and blue arrows in a Cartesian grid with diagonal lines (of slope -1 such that + =. on these diagonal lines) spaced 4 liters apart, both horizontally and vertically.
Alligation is an old and practical method of solving arithmetic problems related to mixtures of ingredients. There are two types of alligation: alligation medial, used to find the quantity of a mixture given the quantities of its ingredients, and alligation alternate, used to find the amount of each ingredient needed to make a mixture of a given quantity.
Read from left to right as a series of numbers that are always divided by four (or by two if you alternate between the top and bottom rows). 96 ÷ 4 = 24; 24 ÷ 4 = 6 (or 06); 48 ÷ 4 = 12 ...
For example, if there are 10 grams of salt (the solute) dissolved in 1 litre of water (the solvent), this solution has a certain salt concentration . If one adds 1 litre of water to this solution, the salt concentration is reduced. The diluted solution still contains 10 grams of salt (0.171 moles of NaCl).
The following formulas can be used to calculate the volumes of solute (V solute) and solvent (V solvent) to be used: [1] = = where V total is the desired total volume, and F is the desired dilution factor number (the number in the position of F if expressed as "1/F dilution factor" or "xF dilution"). However, some solutions and mixtures take up ...
This is denoted as 20 / 5 = 4, or 20 / 5 = 4. [2] In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient. Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend; for example, 10 / 3 leaves a remainder of 1, as 10 is not a multiple of 3.
The largest number that the divisor 4 can be multiplied by without exceeding 5 is 1, so the digit 1 is put above the 5 to start constructing the quotient. Next, the 1 is multiplied by the divisor 4, to obtain the largest whole number that is a multiple of the divisor 4 without exceeding the 5 (4 in this case).
A balance puzzle or weighing puzzle is a logic puzzle about balancing items—often coins—to determine which one has different weight than the rest, by using balance scales a limited number of times. The solution to the most common puzzle variants is summarized in the following table: [1]