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/