## Explanation

You might wonder why we aren't using COUNTIF or COUNTIFS. These functions seem like the obvious solution. However, without adding a helper column that contains a weekday value, there is no way to create criteria for COUNTIF to count weekdays in a range of dates. Instead, we use the versatile SUMPRODUCT function, which handles arrays gracefully without the need to use Control + Shift + Enter. We are using SUMPRODUCT with just one argument, which consists of this expression:

```
--(WEEKDAY(dates,2)=E5)
```

Working from the inside out, the WEEKDAY function is configured with the optional argument 2, which causes it to return numbers 1-7 for the days Monday-Sunday, respectively. This makes it easier to list the days in order with the numbers in column E in sequence. WEEKDAY evaluates each date in **dates** (B5:B15) and returns a number. Because we are giving WEEKDAY 11 dates, we get back an array that contains 11 results like this:

```
{6;1;1;6;3;7;5;6;5;3;2}
```

Each number in this array corresponds to a day of the week, with Mondays equal to 1 and Sundays equal to 7. Next, the numbers returned by WEEKDAY are compared to the value in E5, which is 1:

```
{6;1;1;6;3;7;5;6;5;3;2}=1
```

The result is an array of TRUE/FALSE values like this:

```
{FALSE;TRUE;TRUE;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE;FALSE}
```

In this array, TRUE corresponds to dates that fall on Monday and FALSE represents other days of the week. SUMPRODUCT only works with numbers (not text or Booleans) so we use a double-negative (--) to coerce the TRUE/FALSE values to 1s and 0s. The result is delivered directly to the SUMPRODUCT function:

```
=SUMPRODUCT({0;1;1;0;0;0;0;0;0;0;0}) // returns 2
```

With just one array to process, SUMPRODUCT sums the items and returns 2 as a final result, since there are two Mondays in the dates.

### Dealing with blank dates

If you have blank cells in the list of dates, you will get incorrect results, since the WEEKDAY function will return a result even when there is no date. To handle empty cells, you can adjust the formula as follows:

```
=SUMPRODUCT((WEEKDAY(dates,2)=E5)*(dates<>""))
```

Multiplying by the expression (dates<>"") is one way to "cancel out" empty cells.

### Without day numbers

The day numbers in column E make the formula easier to understand and write. However, since the day names are already in the range D5:D11, which is named **days**, it is possible to write a formula that doesn't use column E at all by using the MATCH function like this:

```
=SUMPRODUCT(--(WEEKDAY(dates,2)=MATCH(D5,days,0)))
```

This works because the MATCH function simply returns the position of each day name in **days**:

```
MATCH(D5,days,0) // returns 1
MATCH(D6,days,0) // returns 2
MATCH(D7,days,0) // returns 3
```

Otherwise, the formula works the same way and returns the same counts as the original formula.