There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular-skilled employees (RE). During the next five months, the division has to complete five projects every month. Out of the 25 projects, 5 projects are "challenging", while the remaining ones are "standard". Each of the challenging projects has to be completed in different months. Every month, five teams - T1, T2, T3, T4 and T5, work on one project each. T1, T2, T3, T4 and T5 are allotted the challenging project in the first, second, third, fourth and fifth month, respectively. The team assigned the challenging project has one more employee than the rest.

In the first month, T1 has one more SE than T2, T2 has one more SE than T3, T3 has one more SE than T4, and T4 has one more SE than T5. Between two successive months, the composition of the teams changes as follows:
a. The team allotted the challenging project, gets two SE from the team which was allotted the challenging project in the previous month. In exchange, one RE is shifted from the former team to the latter team.
b. After the above exchange, if T1 has any SE and T5 has any RE, then one SE is shifted from T1 to T5, and one RE is shifted from T5 to T1. Also, if T2 has any SE and T4 has any RE, then one SE is shifted from T2 to T4, and one RE is shifted from T4 to T2.

Each standard project has a total of 100 credit points, while each challenging project has 200 credit points. The credit points are equally shared between the employees included in that team.

The number of times in which the composition of team T2 and the number of times in which composition of team T4 remained unchanged in two successive months are:

The correct option is B ((1, 0)).

Let us analyze the step-by-step composition of the teams in terms of the number of Special-Skilled Employees (SE) and Regular-Skilled Employees (RE) over the five months.
Total employees = 21 (10 SE, 11 RE).
Each standard team has 4 members, while the team assigned to the challenging project has 5 members (one more than the rest).
For Month 1:
T1 gets the challenging project (size 5). T2, T3, T4, T5 have size 4.
Let the number of SEs in T1, T2, T3, T4, T5 be $s_1,s_2,s_3,s_4,s_5$ respectively.
We are given:
$s_1=s_2+1$
$s_2=s_3+1$
$s_3=s_4+1$
$s_4=s_5+1$
Sum of SEs: $s_1+s_2+s_3+s_4+s_5=10$.
Substituting the equations:
$(s_5+4)+(s_5+3)+(s_5+2)+(s_5+1)+s_5=10$
$5s_5+10=10\Rightarrow s_5=0$.
Thus, the number of SEs in Month 1 is:
T1 = 4, T2 = 3, T3 = 2, T4 = 1, T5 = 0.
The number of REs in Month 1 (since sizes are 5, 4, 4, 4, 4 respectively) is:
T1 = 1, T2 = 1, T3 = 2, T4 = 3, T5 = 4.

Now let's trace the month-to-month transitions using rules (a) and (b):

Month 1 to Month 2:
- T2 gets the challenging project. Rule (a): T2 gets 2 SEs from T1 (challenging team in Month 1) and in exchange, T1 gets 1 RE from T2.
After Rule (a):
T1 SE: 4 - 2 = 2. T1 RE: 1 + 1 = 2.
T2 SE: 3 + 2 = 5. T2 RE: 1 - 1 = 0.
T3, T4, T5 remain unchanged.
- Rule (b):
If T1 has SE (2 > 0) and T5 has RE (4 > 0): 1 SE shifts from T1 to T5, and 1 RE shifts from T5 to T1.
New T1: SE = 1, RE = 3.
New T5: SE = 1, RE = 3.
If T2 has SE (5 > 0) and T4 has RE (3 > 0): 1 SE shifts from T2 to T4, and 1 RE shifts from T4 to T2.
New T2: SE = 4, RE = 1.
New T4: SE = 2, RE = 2.
Thus, Month 2 composition:
T1: (1, 3)
T2: (4, 1)
T3: (2, 2)
T4: (2, 2)
T5: (1, 3)

Month 2 to Month 3:
- T3 gets the challenging project. Rule (a): T3 gets 2 SEs from T2 and in exchange T2 gets 1 RE from T3.
After Rule (a):
T2 SE: 4 - 2 = 2. T2 RE: 1 + 1 = 2.
T3 SE: 2 + 2 = 4. T3 RE: 2 - 1 = 1.
Other teams remain unchanged.
- Rule (b):
If T1 (1, 3) has SE and T5 (1, 3) has RE: 1 SE from T1 to T5, and 1 RE from T5 to T1.
New T1: SE = 0, RE = 4.
New T5: SE = 2, RE = 2.
If T2 (2, 2) has SE and T4 (2, 2) has RE: 1 SE from T2 to T4, and 1 RE from T4 to T2.
New T2: SE = 1, RE = 3.
New T4: SE = 3, RE = 1.
Thus, Month 3 composition:
T1: (0, 4)
T2: (1, 3)
T3: (4, 1)
T4: (3, 1)
T5: (2, 2)

Month 3 to Month 4:
- T4 gets the challenging project. Rule (a): T4 gets 2 SEs from T3 and in exchange T3 gets 1 RE from T4.
After Rule (a):
T3 SE: 4 - 2 = 2. T3 RE: 1 + 1 = 2.
T4 SE: 3 + 2 = 5. T4 RE: 1 - 1 = 0.
Other teams remain unchanged.
- Rule (b):
Since T1 has 0 SE, no exchange between T1 and T5 occurs.
Since T2 (1, 3) has SE and T4 (5, 0) has RE = 0: no exchange between T2 and T4 occurs (T4 has 0 RE).
Thus, Month 4 composition:
T1: (0, 4)
T2: (1, 3)
T3: (2, 2)
T4: (5, 0)
T5: (2, 2)

Month 4 to Month 5:
- T5 gets the challenging project. Rule (a): T5 gets 2 SEs from T4 and in exchange T4 gets 1 RE from T5.
After Rule (a):
T4 SE: 5 - 2 = 3. T4 RE: 0 + 1 = 1.
T5 SE: 2 + 2 = 4. T5 RE: 2 - 1 = 1.
Other teams remain unchanged.
- Rule (b):
Since T1 has 0 SE, no exchange between T1 and T5 occurs.
If T2 (1, 3) has SE and T4 (3, 1) has RE: 1 SE from T2 to T4, and 1 RE from T4 to T2.
New T2: SE = 0, RE = 4.
New T4: SE = 4, RE = 0.
Thus, Month 5 composition:
T1: (0, 4)
T2: (0, 4)
T3: (2, 2)
T4: (4, 0)
T5: (4, 1)

Let us check how many times the compositions of T2 and T4 remained unchanged between successive months:
Team T2:
- Month 1 to 2: Changed from (3, 1) to (4, 1)
- Month 2 to 3: Changed from (4, 1) to (1, 3)
- Month 3 to 4: Month 3 is (1, 3), Month 4 is (1, 3). Unchanged (1 time).
- Month 4 to 5: Changed from (1, 3) to (0, 4)
So T2 remained unchanged 1 time.

Team T4:
- Month 1 to 2: Changed from (1, 3) to (2, 2)
- Month 2 to 3: Changed from (2, 2) to (3, 1)
- Month 3 to 4: Changed from (3, 1) to (5, 0)
- Month 4 to 5: Changed from (5, 0) to (4, 0)
So T4 remained unchanged 0 times.

Thus, the number of times they remained unchanged is (1, 0).