Formula Forensics No. 005 – Zebras and Checker-Boards

Formula Forensics No. 005 – Zebras and Checker-Boards:
This week in Formula Forensics we’ll look at, Zebra Stripes and Checker-board Conditional Formatting.
This idea is inspired by a number of posts over the past few years asking about zebra stripes but specifically BobR who in in June 2011, also asked about Checkerboards in the post: Want to be an excel conditional-formatting Rock Star, Comment No. 154.
I got the conditional format for alternating row and column colors,
Is there a conditional format to make it a checkerboard whereas the cell A2 will remove either the conditional for the row or column and then alternately to A4, B1, B3 etc?



Chandoo responded fairly quickly with this Conditional Formatting formula:
=IF(MOD(ROW(),2)=1,MOD((ROW()-1)*8+COLUMN(),2)=0,MOD((ROW()-1)*8+COLUMN(),2)=1)
Unbeknownst to Chandoo I posted this about a minute later:
=ISODD(ROW()+COLUMN())
Both formula correctly answer BobR’s question.
So today we’re going to pull apart Zebra Stripes and Checker Boards and see what makes them tick.
As always you can follow along in a download file here: Download File.

ZEBRA STRIPES

Zebra Stripes as Conditional Formatting is simply applied using a simple formula within Conditional Formatting.
=MOD(ROW(),2)=0
Conditional Formatting requires a formula that returns a boolean “True” to apply a format or a Boolean “False” to not Apply a format.
So the formula is better read as: If MOD(ROW(),2)=0
And  If MOD(ROW(),2)=0, the formula will evaluate as True
This is best evaluated as 3 columns on a worksheet.

In cells
B5:B10 The formula =Row() returns the Row Number
C5:C10 The formula =Mod(Row() ,2) returns the Mod of Row Number, divided by 2
The Mod function returns the remainder of the division of the Row Number divided by 2,
So in Row 5, Mod(Row(),2) = Mod(5, 2) = 5/2 = 2 Remainder 1 = 1
and in Row 6, Mod(Row(),2) = Mod(6, 2) = 6/2 = 3 Remainder 0 = 0
D5:D10 The formula =Mod(Row() ,2)=0 checks the remainder against the value 0
This is what evaluates to either True or False depending on the Row number.
Where the Values are True the Format will be applied (Even Rows)

The Conditional Formatting can be applied to Odd Rows If the Formula is slightly altered
=Mod(Row() ,2)=1


Similarly the formatting can be applied to Columns using
=MOD(COLUMN(),2)=0/1

CHECKER BOARDS

RobR received two responses to his Checker-Board Conditional Formatting request.
=IF(MOD(ROW(),2)=1,MOD((ROW()-1)*8+COLUMN(),2)=0,MOD((ROW()-1)*8+COLUMN(),2)=1)
and
=ISODD(ROW()+COLUMN())
Lest see what’s inside these two formula.

=IF(MOD(ROW(),2)=1,MOD((ROW()-1)*8+COLUMN(),2) =0, MOD( (ROW() -1)*8+COLUMN(),2)=1)

This is a simple If Formula with 3 components
=IF(MOD(ROW(),2)=1,MOD((ROW()-1)*8+COLUMN(),2)=0,MOD((ROW()-1)*8+COLUMN(),2)=1)
If Condition        MOD(ROW(),2)=1
Value if True:     MOD((ROW()-1)*8+COLUMN(),2)=0
Value if False:    MOD((ROW()-1)*8+COLUMN(),2)=1
The If Condition is already known to us, as it’s the same formula used in the Zebra Stripes above.
It evaluates to True when it is on an Odd Row.
So when it is an Odd numbered Row Excel will look at MOD((ROW()-1)*8+COLUMN(),2)=0
And when it is an Even numbered Row Excel will look at MOD((ROW()-1)*8+COLUMN(),2)=1
We can notice that these are the same formulas which have a different ending of =0 and =1
MOD((ROW()-1)*8+COLUMN(),2)=0
This section Takes each Row subtracts 1 and then multiplies this number by 8. This can be expressed as simply as saying multiply the Row * 8.
This will always return an Even Number and could have been simplified to Row()*2
MOD((ROW()-1)*8+COLUMN(),2)=0
The next bit adds the column number to the previous Even Number.
So now this part will be Odd when the column is Odd and Even when the column is Even.
MOD((ROW()-1)*8+COLUMN(),2)=0
The remainder of the formula is the same as the Zebra Stripes formula.
An Odd Number (Odd Columns) in the section above will return a 1 as the result of =Mod(Odd,2)
An Even Number (Even Columns) in the section above will return a 0 as the result of =Mod(Odd,2)
When evaluated against 0 will return True for Even Columns and False for Odd Columns.
Now the exact same happens in the False section of the If formula except that it is evaluated against 1.

=ISODD(ROW()+COLUMN())

I tackled this problem from a different direction to Chandoo.
Knowing that Even + Even = Even and Even + Odd = Odd and that the row and Column Numbers increase in each direction by 1 each Row/Column, it was simply a matter of adding the Row and Column numbers together and checking if it was Odd or Even
The Excel function IsOdd() and IsEven() both return a Boolean “True” if the contents are Odd or “Even” respectively. This negates an external truth check as described above.
This is easily shown by adding a formula to the Checker area
=Row()+Column()

Excel 2003: The above formula won’t work in Excel 2003.
Try this instead =Mod(Row()+Column(),2)=1



If the alternate shading is required a switch to
=ISEVEN(ROW()+COLUMN())
Does the trick.

Excel 2003: The above formula won’t work in Excel 2003.
Try this instead =Mod(Row()+Column(),2)=0

Learn More About Conditional Formatting Here:

http://chandoo.org/wp/2009/03/13/excel-conditional-formatting-basics/
and
http://chandoo.org/wp/2008/03/13/want-to-be-an-excel-conditional-formatting-rock-star-read-this/
and
http://chandoo.org/wp/2008/10/14/more-than-3-conditional-formats-in-excel/

DOWNLOAD

You can download a copy of the above file and follow along, Download Here.

OTHER POSTS IN THIS SERIES

You can learn more about how to pull Excel Formulas apart in the following posts
Formula Forensics 001 – Tarun’s Problem
Formula Forensics 002 – Joyce’s Question
Formula Forensics 003 – Lukes Reward
Formula Forensics 004 – Freds Problem

We Need Your Help !

If you have a neat formula that you would like to share and explain, try putting pen to paper and draft up a Post as Luke did in Formula Forensics 003. or this post.
If you have a formula that you don’t understand and would like explained but don’t want to write a post also send it in to Chandoo or Hui.