Proof that More People Solve Problems Faster and More Efficiently


In Leadership, it is proven by experience and by common sense that, if you have (for example) 50 problems to solve for a team of (again for example) 10 people in a given time (say 4 months) the team can solve the 50 problems much faster and more efficiently compared to when you give 5 problems to each member of the team (and each member works on their own 5 issues only).

For those who need numbers to believe this, here is the proof:

Proof

Let X be the number of problems,

n be the total number of the team and

t be the time taken to complete a task by an employee

We wish to show that a can be accomplished faster and more efficiently compared to when you divide the task equally among each employee;

  • 50>10*(5) where 50 is the number of tasks to be accomplished, and 10 is the number of employees. 5 is the number of tasks divided within each employee; 50/10

For the first case, the task to be done = x

Assuming that t is directly proportional to x

for the second case, the task to be done = x/n +x/n + x/n+….+x/n =

Using induction method, we wish to proof that >n

Take x/n =I,    

Theorem:

For all fixed nN,

For 1 step summation of 1,

=1(2)/2

Solving by induction process, . Now consider

= +n+1

=

This therefore is a proof that by induction, the theorem holds.

We recall our i=x/n

=

For 1 step, = 1(2)/2 =1

For 2 = 2(3)/2 = 3, for 3=3(4)/2 =6



Say n =10 and x=50,

Then x/n =5


= 30/2

=15 which is greater than 5.

Recall that t is directly proportional to x; therefore, it will be faster for the problems to be solved by a team within a given time period compared to dividing the problems within the group.

Aref Karimi

https://www.linkedin.com/in/arefkarimi/

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