No Rule for Seven - Fun with Numbers
Miles Goldstein
Global Product / Technical Support Leader- Enterprise Software | SaaS
No Rule for Seven – Fun with Numbers – D M Goldstein, April 2024
I have always liked numbers. I did well in Math in grade school and I was a Mathematics major for a brief time in college before switching to Computer Science. One piece of trivia I picked up along the way is that there is a simple rule for determining whether an integer is completely divisible (no fractions, decimals, or remainders) by each of the numbers one through nine, except for seven; there is no rule for seven. In this article I will share those rules and use those numbers to share insights into Software Support. (Hey, that’s what I do.)
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One
Rule: This is the most obvious one; every integer is divisible by one.
Support Insight: You only get one chance to make a first impression. When your customer reaches out to you, they are usually dealing with an issue. How you approach the customer and the problem sets the stage for your engagement with them, but also possibly for your long-term relationship with them. Are you appropriately sympathetic and diplomatic? Do they feel that you understand them and will take care of them? Are you earning their trust? And are you providing information to set their expectations?
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Two
Rule: One of the first rules we learn in Arithmetic is that if the last (right-most) digit is divisible by two, then the number is “even” and divisible by two.
Support Insight: There are two sides to every customer engagement - your company’s and the customer’s. Be sure that you are being empathetic and truly listening to the customer’s point of view. If you do not understand where they are coming from then you cannot truly solve their problem. Sometimes you must listen closely to determine what the real problem is; it is not always the problem they are presenting to you. “Can I do [this thing] to accomplish [that result]?” is not a yes-or-no question; it is a business problem (“[that result]”) that needs to be addressed.
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Three
Rule: If you add up the digits in a number and the result is a multiple of three, the whole number is divisible by three. You can even iterate until you get an easy total. If you have the number 37,035, add up the digits to get 18. You can then add those digits (if needed) and get 9. Voila. (12345 * 3 = 37035)
Support Insight: In elementary school we learned “the three Rs” as “Reading, wRiting, and ‘Rithmatic.” In Support, I would say the three Rs are Response time, Resolution time, and providing the Right answer. If you fail at any one of them, you will have difficulty recovering. If you fail on Response Time, then “Support is a black hole.” If you fail on Resolution Time, then “Support doesn’t know what they’re doing.” And if you fail on providing the Right Answer, then “Why even bother asking Support?”
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Four
Rule: You only need to look at the two right-most digits and check whether they are divisible by four. If so, then the entire number is.
Support Insight: There are four quarters in your Fiscal Year. That’s a long time and you often must forecast things like your budgets far in advance. Use your data wisely to come up with realistic forecasts and requests. But always be working on a “Plan B” for what you’ll need to do if either your forecast is wrong or other factors (like budgets) change on you. Regardless of whether you do quarterly plan updates, these mileposts are a good reminder to step back and evaluate your progress and make any necessary adjustments.
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Five
Rule: Another basic observation one; if the final digit is zero or five, it is divisible by five.
Support Insight: Many SaaS vendors measure their uptime by “9s”. That’s how many nines are in their percentage availability (“uptime”) number. 99.5% available is “2.5 nines” and basically allows you 7.2 minutes of downtime in a day, or 2628 minutes over the course of a year (43.8 hours). “Three nines” is 99.9%, equating to 1.44 minutes a day, or 525.6 minutes a year (8.76 hours). “Four nines” is 99.99% - 0.144 minutes in a day and only 52.56 minutes in a year. There is an ideal target of five nines, allowing one tenth of that time. Most companies have a hard enough time hitting three nines. Some commit to four nines. “Five nines” gives you just over 5 (five) minutes a year(!), when it often takes longer than that just to realize that you are down. This is where “massive redundancy” helps; every function or server has multiple instances running, so if a single instance fails then work will quietly “fail over” to another instance. This is usually automatic and transparent. This is a fundamental requirement of any SaaS (Software as a Service) product, where you are hosting the application “in the cloud”.
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Six
Rule: This one puts the rules for two and three together. If the digits add up to a multiple of three and the last digit is even, the number is divisible by six.
Support Insight: I wrote an article on “The Problem Resolution Process” (Ref 1). In it I outline the six steps to solving most problems:
1.????? Characterize: what is happening, what is expected, and what was changed?
2.????? Diagnose: drill down to understand the details, verify steps, do critical thinking.
3.????? Research: is this a known situation, is it expected, are there known fixes or workaround?
4.????? Reproduce: if you can’t reproduce you can’t confirm a fix.
5.????? Resolve: provide an answer, explanation, or resolution.
6.????? Verify: did you solve the problem?
As I wrote there, these are a universal set of steps to resolve almost any problem, though it is not always obvious that you are practicing them.
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Seven
Rule: There is No Rule for Seven.*
Support Insight: There may be “no rule for seven”, but there are seven days in a week. How are you going to provide Support to your customers 24x7? Do you have global shifts which “follow the Sun”? Do you have on-call personnel for high-impact problems where expertise is limited? What are your customers’ needs and expectations, and what additional negative impact does a problem have on them if they are required to wait until the start of your next business day before you respond to it? Consider weekdays versus weekends, and whether you handle only high-priority issues outside of your business hours. I go into detail in “On Call, 24x7” (Ref 2).
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Eight
Rule: Like four, you need only evaluate the three right-most digits. If they are divisible by eight, then the whole number is.
Support Insight: In my article “The Seven Rules of Reporting” (Ref 3) I provide eight rules:
1.??????????????? Ask the right questions.
2.??????????????? Context matters.
3.??????????????? Use the appropriate measurement methods.
4.??????????????? Look at trends over time.
5.??????????????? Know what it is you are measuring, and why.
6.??????????????? Only track and report on the items and at a granularity that drives action.
7.??????????????? Reports don’t always answer questions; more often they tell you which questions you should be asking next.
8.??????????????? annotate to aid in understanding.
Presenting numbers without context, or effectively the “wrong” numbers, will have huge negative consequences, especially when being used for forecasting, planning, and budget requests.
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Nine
Rule: Like the rule for three, if the sum of the digits is a multiple of nine then the whole number is. My example of 37,035 adding up to 18 is therefore divisible by nine, whereas 37,032 adds up to 15 so is not divisible by nine but is divisible by three or six.
Support Insight: In “Building the Support Organization” (Ref 4) I identify nine roles or teams that should be part of a mature Support organization:
1.??????????????? Front-line Support (Tier 1)
2.??????????????? Back-line Support (Tier2)
3.??????????????? Support Readiness and Enablement
4.??????????????? Support Operations and Tools (including Support Planning)
5.??????????????? Training
6.??????????????? Knowledge Management
7.??????????????? Escalation Management
8.??????????????? Incident Management
9.??????????????? Special teams and programs
In a small company these might not be discrete teams, but the functions they represent must still be addressed. In a large-enough company there may be even more teams, splitting out some of the above for more focus and specialization.
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A “Numbers Nerd” parlor trick
My father’s uncle taught me a parlor trick, where any three-digit number can be manipulated using basic arithmetic into a series of 5s. For example, 123 can be broken down as “1*(2+3)” which equals 5. 987 becomes “98-7” = 91 and 9+1=10=2*5. For completeness, any ordering of 4,5,6 adds up to 15 (=3*5) or you can get fancy with +4-5+6=5. I have only found one three-digit number where I had to stretch the unwritten rules and use a decimal (.5) as part of my result instead of a pure integer. Hit me up in the comments if you have a number which you think will stump me.
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Post-publication note: A friend has informed me that there is a way to determine whether a number is divisible by 7. You double the last digit at the unit place and subtract that from the rest of the numbers to see if it is divisible by 7. For instance, 476 is a multiple of 7 because 12 (=6*2) subtracted from 47 yields 35, which is a multiple of seven. You can apply this rule iteratively on large numbers until you have a number that is small enough to know is a multiple of 7.
References:
Side note: I was going to use a Calvin and Hobbes cartoon about Math as my graphic, but apparently there are strict copyright restrictions which I will honor by not just using it.
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