**Problem of the Week**

Problem C

How It Ends

The product of the positive integers 1 to 4 is \[4\times 3\times 2\times 1 =24\] and can be written in an abbreviated form as \(4!\). We say “4 *factorial*”. So \(4!=24\).

The product of the positive integers 1 to 16 is \[16\times 15\times 14\times\cdots\times 3\times 2\times 1\] and can be written in an abbreviated form as \(16!\). We say “16 *factorial*”.

The \(\cdots\) represents the product of all the missing integers between 14 and 3.

In general, the product of the positive integers 1 to \(n\) is \(n!\). Note that \(1!=1\). Determine the tens digit and units (ones) digit of the sum \[1!+2!+3!+ \cdots +2019!+2020!+2021!\]

**Strands:** Number Sense and Numeration, Patterning and Algebra