(Enter two values)

Product 112 | ||
---|---|---|

Factor A 56 | Factor B 2 | |

Sum 58 |

Step by Step

We put in your hands the best online **Diamond Problem Solver**, which is an excellent tool to solve diamond problems step by step. To use the calculator, you just have to enter any two values and press the “Calculate” button and the solution will automatically be displayed.

A diamond problem can be seen as a puzzle that is structured in the shape of a rhombus or diamond subdivided into four sections by an x located in the center. In the side sections two numbers called Factor A and Factor B are placed, in the upper section the product of both factors is placed and in the lower section the sum of said factors is placed.

Of these four values, only two are known, so the objective of the diamond problem is to calculate the value of each unknown number.

Depending on what the known numbers are, there are different variants of diamond problems:

Given two factors

Given one factor and the product

- Given one factor and the sum
Given product and sum

Below we will explain how to resolve each of the aforementioned cases. To do this we will use examples explained step by step and generated with the help of the Diamond problem solver.

To solve a diamond problem given the two factors, follow the following steps:

- Multiply both factors to obtain the product.
- Add both factors to obtain the sum.

Here is an example generated with the help of the Diamond problem calculator:

Factor A = 8.00

Factor B = 5.00

Product = Format A × Format B

= 8.00 × 5.00

= 40.00

Sum = Format A + Format B

= 8.00 + 5.00

= 13.00

Product 40.00 | ||
---|---|---|

Factor A 8.00 | Factor B 5.00 | |

Sum 13.00 |

If we know the value of one of the factors and the value of the product, the following procedure must be executed:

- Divide the product by the known factor to find the unknown factor.
- Add both factors to calculate the value of the sum.

So that you better understand how to apply this procedure, here we present an example:

Factor B = 3.00

Product = 15.00

Factor A = ProductFactor B

= 15.003.00

= 5.00

Sum = Format A + Format B

= 5.00 + 3.00

= 8.00

Product 15.00 | ||
---|---|---|

Factor A 5.00 | Factor B 3.00 | |

Sum 8.00 |

To solve this type of diamond problem, follow these two simple steps:

- Subtract the value of the known factor from the sum value to obtain the value of the unknown factor.
- Multiply both factors to get the product.

This procedure is very simple to execute, but an example always helps us better understand the concepts:

Factor A = 6.00

Sum = 9.00

Factor B = Sum − Factor A

= 9.00 − 6.00

= 3.00

Product = Format A × Format B

= 6.00 × 3.00

= 18.00

Product 18.00 | ||
---|---|---|

Factor A 6.00 | Factor B 3.00 | |

Sum 9.00 |

To solve a diamond problem in which the sum and the product are given, there are various methods, but our favorite is the one that poses the problem as a quadratic equation:

(*x + Factor A*)(*x + Factor B*)* = 0*

*x ^{2 }+ Sum·x + Product = 0*

The value of the factors will be the same as the value of the roots of the quadratic equation, so we can apply the general formula to calculate the values of the factors. Here is an example that perfectly illustrates how to solve this type of diamond problem:

Product = 12.00

Sum = 7.00

We will obtain Factor A and Factor B by applying the general formula:

Factor A = Sum +√Sum^{2}−4·Product2

= 7.00 +√7.00^{2}−4(12.00)2

= 4.00

Factor B = Sum −√Sum^{2}−4·Product2

= 7.00 −√7.00^{2}−4(12.00)2

= 3.00

Product 12.00 | ||
---|---|---|

Factor A 4.00 | Factor B 3.00 | |

Sum 7.00 |