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.

One of the employees named Aneek scored 185 points. Which of the following CANNOT be true?

The correct option is D.

An employee scoring 185 points must have worked on exactly 4 challenging projects and 1 standard project, since:
Total = 125 + 15c = 185 ⇒ 15c = 60 ⇒ c = 4.

Since the challenging project is completed by T1 in Month 1, T2 in Month 2, T3 in Month 3, T4 in Month 4, and T5 in Month 5, working on 4 challenging projects means Aneek must have worked in the corresponding challenging teams during those 4 months.

Let's check the transition paths for SEs, who can move as follows:
- Through Rule a: T1 → T2 → T3 → T4 → T5 (moves 2 SEs to the new challenging team)
- Through Rule b: T1 → T5 (1 SE) and T2 → T4 (1 SE)

Let's evaluate the options for a sequence of 4 challenging teams:
- Option A (T1, T2, T3, T4): This corresponds to being in the challenging teams in Months 1, 2, 3, and 4. An SE starting in T1 can transition T1 → T2 → T3 → T4 via Rule a. In Month 5, when T5 is challenging, the SE remains in T4 (standard project). This is possible.
- Option C (T2, T3, T4, T5): This corresponds to being in the challenging teams in Months 2, 3, 4, and 5. An SE starting in T2 in Month 1 (which is standard for T2) can transition T2 → T3 → T4 → T5 via Rule a. This is possible.
- Option B (T1, T2, T4, T5): This corresponds to being in the challenging teams in Months 1, 2, 4, and 5. The path would require being in T1 (Month 1, challenging) → T2 (Month 2, challenging) → T4 (Month 3, standard) → T4 (Month 4, challenging) → T5 (Month 5, challenging). An SE can move T2 → T4 via Rule b during the Month 2 to Month 3 transition, stay in T4 in Month 4, and then move T4 → T5 via Rule a. This is possible.
- Option D (T1, T3, T4, T5): This corresponds to being in the challenging teams in Months 1, 3, 4, and 5. This would require a transition from T1 in Month 1 to a team other than T2 in Month 2, and then to T3 in Month 3. The only SE transition from T1 in Month 1 is either to T2 (Rule a) or T5 (Rule b). If the SE moves to T5 in Month 2, they cannot reach T3 in Month 3 because there are no transitions from T5 to T3 for SEs or REs. Thus, this configuration is impossible.