Wire Colors, Phases, and Circuit Numbers – Part 3: Trick Based on Multiples of Six

In parts 1 and 2 of this series, we learned the basics of two different methods to find on which phase a circuit number is.  Those methods relied upon division and subtraction.  I personally find it much easier to use addition as much as possible when doing math in my head as it is the easiest to do.  This next method does use subtraction, but we will only be subtracting either the number 3 or the number 6.

Again, here are our tables from part 2:

120/208/240 Volts:

277/480 Volts:

This method is based on the fact that multiples of six repeat in a special pattern over our base 10 numbering system (which will be discussed a little in part 4).  I discovered this trick a couple of months ago when I was looking closely at the system I used for the past year and a half (which is the method in part 4) and this method is a sort-of short-cut of that.  It is very simple once one has used it a few times and usage will improve with practice.  Here are the guidelines:

1. Take note of whether the circuit number is odd or even.
2. Add the digits of the circuit number together until you have a single digit.
3. Compare the single digit’s oddness or evenness to the circuit number’s oddness or evenness and do the following to bring the single digit to 6 or less:
   • If both the circuit number and the single digit are odd or if both are even, either subtract 6 or subtract nothing if the single digit is already 6 or less.
   • If the circuit number is odd and the single digit even or vice versa, then add or subtract 3 from the single digit, whatever is needed to keep the single digit between 1 and 6.
4. Then take the answer and apply it to the tables above to find the phase for the original circuit number.

That may seem difficult and complex, but it gets easier with practice to the point to where it becomes second nature.  Let’s do lots of examples.

We’ll start with circuit 83 that we saw in part 1:

1. First, take note of whether or not the circuit number is odd or even.  83 is odd.
2. Add the digits of the circuit number (83) together until you have a single digit:  8 + 3 = 11.  Because 11 is not a single digit, we add its digits as well: 1 + 1 = 2.
3. Compare the single digit’s oddness or evenness – 2 is even – with the circuit number – 83 is odd.  Because the circuit number and the single digit are not both even or both odd, then we need to add or subtract 3, whichever keeps the single digit between 1 and 6:  2 + 3 = 5.
4. We then look at the table above and see that 5 is on phase C.  Therefore circuit 83 is on phase C.

Another example, circuit 44:

1. 44 is even.
2. 4+4 = 8.
3. 44 is even and 8 is even.  Since both the circuit number and the single digit are even, we need to either subtract 6 or do nothing if the single digit is less than 6.  Because the single digit is more than 6, we need to subtract 6:  8 – 6 = 2.
4. We then look at the table and see that 2 is on phase A.  Therefore circuit 44 is on phase A.

Exampe, circuit 45:

1. 45 is odd.
2. 4 + 5 = 9.
3. 45 is odd and 9 is odd.  Since both are odd and the single digit is more than 6, we subtract 6:  9 – 6 = 3.
4. 3 is on phase B.  Therefore circuit 45 is on phase B.

Example, circuit 46:

1. 46 is even.
2. 4 + 6 = 10.  1 + 0 = 1.
3. 46 and 1 are not both even nor both odd, therefore we need to add or subtract 3 from the single digit to keep it between 1 and 6.  In this case, we need to add 3 to the single digit:  1 + 3 = 4.
4. 4 is on phase B and therefore circuit 46 is on phase B.

Example, circuit 41:

1. 41 is odd.
2. 4 + 1 = 5.
3. 41 and 5 are both odd.  Since 5 is less than 6, we do nothing.
4. 5 is on phase C and therefore circuit 41 is on phase C.

Example, circuit 51:

1. 51 is odd.
2. 5 + 1 = 6.
3. 51 is odd and 6 is even.  Because the circuit and the single digit are not both odd or both even, we need to add or subtract 3, whichever keeps the single digit between 1 and 6:  6 – 3 = 3.
4. 3 is on phase B and therefore circuit 51 is on phase B.

Example, circuit 59:

1. 59 is odd.
2. 5 + 9 = 14, 1 + 4 = 5.
3. 59 is odd and 5 is odd.  Since 5 < 6, we do nothing.
4. 5 is on phase C and therefore 59 is on phase C.

In summary, one just has to:

• remember the oddness or evenness of the circuit number
• add the digits of the circuit number to a single digit
• compare that single digit with the circuit number and add or subtract as needed
• find the phase for the circuit number

Although this is my primary method for finding the phase for a circuit number, this method may not click with you.  If not, use one of the other methods listed in this series of articles.

In part 4 of this series, we will discuss the original method I used until I discovered the method listed here in part 3.

Table of Contents

• Part 1:  Introduction and Long Division
• Part 2:  Subtracting Multiples of Six
• Part 3:  Trick Based on Multiples of Six (this article)
• Part 4:  Original Method Based on Multiples of Six