Descendingly Arrange Items in a List

Sort a list in descending order using the Function in the complete example code. The output will show the sorted list. Another option to sort the list in descending order is to use the LINQ Library. Question: For Project Euler , the task requires me to analyze a descending order consisting of numbers with three […]

Identifying Leap Years in 2000

The number of non-leap years under the newer Gregorian calendar, which is explained in your question, needs to be determined. An alternative method to find the answer is to calculate $$ {2000over4}-{2000over100}+{2000over400}-1 $$ This approach assumes that every fourth year is a leap year and includes the year 2000. Solution 1: Before the adoption of […]

Finding Inverses Using Exponentiation Method: A Guide

An example of this can be seen in the following equations: $begin{cases}&log_3x=yiff 3^y=x\&3^y=xiff log_3x=yend{cases}$. It is now evident that $f(x):=log_ax$ and $g(x):=a^x$ are inverse functions. This means that $fcirc g(x)=f(g(x))=log_a(a^x)=x=3^{log_ax}=g(f(x))=gcirc f(x)$. To simplify this concept for a layman, we can use integers and the $log_{10}$ method. For instance, $pmod{17}$ and $(-4)^2equiv -1$. Question: I’m feeling […]

Calculating the quantity of whole number solutions to equations using the inclusion-exclusion principle

The number of non-negative integral solutions for positive integers $x_1$, $x_2$, $x_3$, $x_4$, and $x_5$, with a maximum value of 5, is 365, as calculated by subtracting 350 from 715. Solution 2: The number of non-negative integer solutions for $X1+X2+…+XK=N$ is equivalent to the number of ways to distribute n identical balls into k labeled […]