Here is an interesting problem to start your day.
Let’s say you work as DNA sequencing engineer at The Enterprise. And you just unlocked the sequence that is responsible for all male problems. The early onset of baldness. The sequence code is AAAA. And you want to find out how many times this sequence is found in a sample of DNA strings, in the range B6:B19. Essentially you want this:
So how do you write the formula?
Counting occurrences using Excel formulas
We can use LEN() and SUBSTITUTE() formulas to solve this problem.
Let’s say your target to find is in $C$3 and the full sequence is in B6. We can use below formula to find how many times C3 is present in B6.
=(LEN(B6) - LEN(SUBSTITUTE(B6,$C$3,""))/LEN($C$3)
How does this formula work?
Let’s go inside out (said male baldness to the head):
SUBSTITUTE(B6,$C$3,””): This replaces all occurrences of C3 in B6 with empty string.
LEN(SUBSTITUTE(…)): This will return the length of new text after replacing all C3s in B6.
LEN(B6): this simply gives us the length of original text
LEN(B6)-LEN(SUBSTITUTE(…)): Will give us the count of total letters replaced.
(LEN(..)-LEN(..))/LEN($C$3): Tells us how many times C3 is present in B6.
So there you go.
Download Example Workbook:
Click here to download the example workbook. Play with the formulas to learn more.
A challenge for you – Find total occurrence count with single formula:
Let’s say you want to find out how many times $C$3 is present in a range – B6:B19 with one formula. How would you write it?
Please post your answers in comments section.
Related formulas:
Check out below examples to learn more.
- Array formula to count maximum text occurrences in a range
- How to count words in a cell using formulas
- How many times a list of values occurs in another list?
- VLOOKUP based on pattern
PS: Thanks to Simran who emailed me this question.
PPS: The writer is not balding. He still sports plenty of pointy hair 🙂
14 Responses to “How many ‘Friday the 13th’s are in this year? [Formula fun + challenge]”
in C3=2016
in C4=3
in C5=1 (the first next year with three Friday the 13ths)
=SMALL(IF(MMULT(--(MOD(DATE(C3+ROW(1:1000),COLUMN(A:L),13),7)=6),ROW(1:12)^0)=C4,C3+ROW(1:1000)),C5)
formula check in the next 1000 years
This will generate a table of counts of Friday the 13th's by year. If I didn't screw it up the next year with three is 2026.
I created a simple parameter table with a start date and end date that I wanted to evaluate. That calculates the number of days and generates a list of those days. Then filter and group. The generation of the list in power query (i.e. without populating a date table in excel) is pretty cool, otherwise this isn't really doing anything than creating a big date and filtering/counting.
let
Source = List.Dates(StartDateAsDate, Days2, #duration(1,0,0,0)),
ConvertDateListToTable = Table.FromList(Source, Splitter.SplitByNothing(), null, null, ExtraValues.Error),
AddDayOfMonthColumn = Table.AddColumn(ConvertDateListToTable, "DayOfMonth", each Date.Day([Column1])),
AddYearColumn = Table.AddColumn(AddDayOfMonthColumn, "Year", each Date.Year([Column1])),
AddDayOfWeekColumn = Table.AddColumn(AddYearColumn, "Day of Week", each Date.DayOfWeek([Column1])),
FilterFriday13 = Table.SelectRows(AddDayOfWeekColumn, each ([DayOfMonth] = 13) and ([Day of Week] = 5)),
Friday13thsByYear = Table.Group(FilterFriday13, {"Year"}, {{"Number of Friday the 13ths!", each Table.RowCount(_), type number}})
in
Friday13thsByYear
With the parameters replaced by values should you want to play along at home. This runs for 20 years starting on 1/1/2016.
let
Source = List.Dates(#date(2016,1,1), 7300, #duration(1,0,0,0)),
ConvertDateListToTable = Table.FromList(Source, Splitter.SplitByNothing(), null, null, ExtraValues.Error),
AddDayOfMonthColumn = Table.AddColumn(ConvertDateListToTable, "DayOfMonth", each Date.Day([Column1])),
AddYearColumn = Table.AddColumn(AddDayOfMonthColumn, "Year", each Date.Year([Column1])),
AddDayOfWeekColumn = Table.AddColumn(AddYearColumn, "Day of Week", each Date.DayOfWeek([Column1])),
FilterFriday13 = Table.SelectRows(AddDayOfWeekColumn, each ([DayOfMonth] = 13) and ([Day of Week] = 5)),
Friday13thsByYear = Table.Group(FilterFriday13, {"Year"}, {{"Number of Friday the 13ths!", each Table.RowCount(_), type number}})
in
Friday13thsByYear
=MATCH(3,MMULT(N(WEEKDAY(DATE(C3+ROW(1:100)-1,COLUMN(A:L),13))=6),1^ROW(1:12)),)+C3-1
It should be pointed out that Alex's solution, unlike some others, has the additional advantage of being non-array. My solution was nearly identical but with -- and SIGN instead of N and 1^.
=C3-1+MATCH(3,MMULT(--(WEEKDAY(DATE(C3-1+ROW(1:25),COLUMN(A:L),13))=6),SIGN(ROW(1:12))),0)
Sub Friday13()
Dim StartDate As Date
Dim EndDate As Date
Dim x As Long
Dim r As Long
Range("C7:C12").ClearContents
StartDate = CDate("01/01/" & Range("C3"))
EndDate = CDate("31/12/" & Range("C3"))
r = 7
For x = StartDate To EndDate
If Day(x) = 13 And Weekday(x, vbMonday) = 5 Then
Cells(r, 3) = Month(x)
r = r + 1
End If
Next
End Sub
Calculate next year with 3 Friday 13th. Good for 100 years different from year entered in cell C3
Sub ThreeFriday13()
Dim StartDate As Date
Dim EndDate As Date
Dim x As Long
Dim WhatYear As Integer
Dim Counter As Integer
Range("E7").ClearContents
StartDate = CDate("01/01/" & Range("C3") + 1)
EndDate = CDate("31/12/" & Range("C3") + 100)
Counter = 0
For x = StartDate To EndDate
If WhatYear Year(x) Then
WhatYear = Year(x)
'Different year so reset counter
Counter = 0
End If
If Day(x) = 13 And Weekday(x, vbMonday) = 5 Then
Counter = Counter + 1
If Counter = 3 Then
WhatYear = Year(x)
Exit For
End If
End If
Next
Range("E7") = WhatYear
End Sub
*RE-POST as not equal did not show earliuer
Calculate next year with 3 Friday 13th. Good for 100 years different from year entered in cell C3
Sub ThreeFriday13()
Dim StartDate As Date
Dim EndDate As Date
Dim x As Long
Dim WhatYear As Integer
Dim Counter As Integer
Range("E7").ClearContents
StartDate = CDate("01/01/" & Range("C3") + 1)
EndDate = CDate("31/12/" & Range("C3") + 100)
Counter = 0
For x = StartDate To EndDate
If WhatYear NE Year(x) Then
WhatYear = Year(x)
'Different year so reset counter
Counter = 0
End If
If Day(x) = 13 And Weekday(x, vbMonday) = 5 Then
Counter = Counter + 1
If Counter = 3 Then
WhatYear = Year(x)
Exit For
End If
End If
Next
Range("E7") = WhatYear
End Sub
earlier*
I've a doubt with using array formula here.
In sample workbook, I tried to replicate the formula again.
=IFERROR(SMALL(IF(WEEKDAY(DATE($C$3,ROW($A$1:$A$12),13))=6,ROW($A$1:$A$12)),$B7),"")
For this I selected C7 to C12, and typed the same formula and pressed ctrl+alt+Enter. But in all cells it is taking $B7 (and not $B7, $B8, $B9.... etc)
and since it is array formula I can't edit individual cell.
Please guide.
Thanks
Hi Chandoo,
Cool stuff. You need to clarify that the answer of 5 represents the 1st month in the year that has a Friday the 13th, and not the number of Fridays the 13th in the year. Subtle, but important difference.
Thanks,
Pablo
I like the MMULT() function far more, but here's how I would have tackled it. It uses an EDATE() base and MODE() over 100 years. I'm assuming that 100 years is enough time to catch the next year with 3 friday 13th's. Array entered, of course.
{=MODE(IFERROR(YEAR(IF((WEEKDAY(EDATE(DATE(C3, 1, 13), ROW(INDIRECT("1:1200"))))=6), EDATE(DATE(C3, 1, 13), ROW(INDIRECT("1:1200"))), "")), ""))}
Finding all the Friday the 13ths in a Year:
=SUMPRODUCT((DAY(ROW(INDIRECT(DATE(C3,1,1)&":"&DATE(C3,12,31))))=13)*(TEXT(ROW(INDIRECT(DATE(C3,1,1)&":"&DATE(C3,12,31))),"ddd")="Fri"))
{=sum(if(day.of.week(DATe($YEAR;{1;2;3;4;5;6;7;8;9;10;11;12};13);1)=6;1;0))}
just list the years