So can you help me find answer?

A for effort was given to a colleague who answer this correctly and I can clearly see why. He answered it very thoroughly and I am going to publish it with due credits to him (name not published for privacy).

As he wrote:

“The series given was 3, 11, 20, 27, 29, 23

The solution, the way I saw it was to find some function, f(x) that would equal:

f(1) = 3, f(2) = 11, f(3) = 20, etc

so that I could predict the value of f(7).

I found the differences between each set of answers to go down 3 levels, with a shared difference of -3.  Three levels means I need to find a third degree polynomial  f(x) = ax^3 + bx^2 + cx + d.

I then needed to find the values for a, b, c and d.  There are 4 unknowns, so I need 4 equations.

The four equations are:

f(1) = a(1)^3 + b(1)^2 + c(1) + d = 3

f(2) = a(2)^3 + b(2)^2 + c(2) + d = 11

f(3) = a(3)^3 + b(3)^2 + c(3) + d = 20

f(4) = a(4)^3 + b(4)^2 + c(4) + d = 27

Using linear algebra and putting these into a matrix and reducing to echelon form, I solved for a, b, c and d.

a=-1/2, b=7/2, c=1, d=-1

That makes f(x) = -1/2 x^3 + 7/2 x^2 + x – 1

Calculating out f(x):

X	-1/2 x^3	7/2 x^2	X	-1	f(x)
0	0	0	0	-1	-1
1	-0.5	3.5	1	-1	3
2	-4	14	2	-1	11
3	-13.5	31.5	3	-1	20
4	-32	56	4	-1	27
5	-62.5	87.5	5	-1	29
6	-108	126	6	-1	23
7	-171.5	171.5	7	-1	6
8	-256	224	8	-1	-25
9	-364.5	283.5	9	-1	-73

Finally, the answer to the question is 6, highlighted above in red.”

What does it mean to you? Avoid longer commute? Work from home? Work flexible schedules?

You can read some interesting facts at Wikipedia link above.

At Microsoft, we are reminded to think about our Work-Life blend and prioritize work to limit interruptions and its ripple effects. It means keeping realistic workloads, taking a proactive approach and when reactive or crisis-centered events prolong the workday, utilizing the vast knowledge and resources from within the company.

When one of my colleagues asked for help for few hours this week with his customer, I was happy to take the opportunity and do what I can. I am sure this helped out my colleague when he needed it and I know I have the same support from entire PFE community if I ever need.

This is what I like about working at company like Microsoft who really provide the resources to achieve the balance you need to make your life complete. It can mean that extra hour you can spend at your kid’s game or take your wife out to that Broadway show. Or it can simply mean stay home and do nothing for people like me.

Quote of the day:
No man needs a vacation so much as the man who has just had one. – Elbert Hubbard