Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year. In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.

The following additional facts are known.

1. Ustad Samiran never trained more than one of these students in the same year.

2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.

3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years. 4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively

In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus?

The correct answer is 4.

To solve this logical puzzle, we must determine the training schedule for the four musicians: Ananya (A), Bhaskar (B), Charu (C), and Devendra (D) under the three Gurus: Pandit Meghnath (P), Ustad Samiran (U), and Acharya Raghunath (R) over the 12 years from 2013 to 2024.

Step 1: Determine the training span for each Guru
We are given that each Guru has a different training span of 2, 3, or 4 consecutive years. Acharya Raghunath (R) did not train any students during 2015-2018 and 2021-2024. This leaves only the years 2013, 2014, 2019, and 2020 available for Guru R. Since training requires consecutive years, these available years form two blocks of exactly 2 years each (2013-2014 and 2019-2020). Therefore, the training span for Guru R must be exactly 2 years.

Step 2: Identify the Gurubhai pairings
A "Gurubhai" pair is formed when two students train under the same Guru at the same time. We know that A and D were never Gurubhai, and B and C were never Gurubhai. All other pairs were Gurubhai for exactly 2 years. These valid pairs are: (A, B), (A, C), (B, D), and (C, D).

Ustad Samiran (U) never trained more than one student in the same year, which means no Gurubhai pairs could ever be formed under Guru U. Consequently, all Gurubhai overlaps must have occurred under either Guru P or Guru R.

Step 3: Assign students to Guru R (Acharya Raghunath)
We know A started training under P in 2013, and B started under U in 2013. Because a student cannot train under multiple Gurus in the same year, neither A nor B could have trained under R in the initial 2013-2014 block. Therefore, C and D must be the two students who trained under R in 2013 and 2014. This forms the (C, D) Gurubhai pair for 2 years.

Since each of the four musicians must train under every Guru, A and B must take the other available 2-year block for Guru R, which is 2019 and 2020. This forms the (A, B) Gurubhai pair for exactly 2 years.

Step 4: Determine the span and schedule for Guru P (Pandit Meghnath)
The remaining Gurubhai pairs that need to be formed are (A, C) and (B, D). These must occur under Guru P. We know A started under Guru P in 2013. For A and C to overlap for exactly 2 years, Guru P's span must be 4 years. (If it were only 3 years, A would train from 2013-2015, leaving only the year 2015 for an overlap with C, since C is busy with R in 2013-2014). Thus, Guru P's span is 4 years, and consequently, Guru U's span is 3 years.

Now we can schedule Guru P (4 years span):
- A trains under P from 2013 to 2016.
- To have a 2-year overlap with A, C must train under P from 2015 to 2018 (overlapping in 2015 and 2016).
- For the (B, D) pair: B started under U from 2013-2015 and is under R from 2019-2020. The only remaining 4-year block for B to train under P is 2021 to 2024.
- To overlap with B for exactly 2 years, D must train under P from 2019 to 2022 (overlapping with B in 2021 and 2022).

Step 5: Schedule the remaining training under Guru U (Ustad Samiran)
Guru U has a span of 3 years and trains students one at a time continuously.
- B started under U from 2013 to 2015.
- D must train under U next. D is available from 2015 onwards, but 2015 is taken by B. Thus, D trains under U from 2016 to 2018.
- C must train under U next. C just finished Guru P in 2018, so C trains under U from 2019 to 2021.
- Finally, A is available to train under U from 2022 to 2024.

Step 6: Count the number of training musicians per year
Now we list which musicians are actively training in each year from 2013 to 2024:
- 2013: A, B, C, D (4 musicians)
- 2014: A, B, C, D (4 musicians)
- 2015: A, B, C (3 musicians)
- 2016: A, C, D (3 musicians)
- 2017: C, D (2 musicians)
- 2018: C, D (2 musicians)
- 2019: A, B, C, D (4 musicians)
- 2020: A, B, C, D (4 musicians)
- 2021: B, C, D (3 musicians)
- 2022: A, B, D (3 musicians)
- 2023: A, B (2 musicians)
- 2024: A, B (2 musicians)

Looking at the year-by-year breakdown, exactly two musicians are training in the years 2017, 2018, 2023, and 2024.

Therefore, there are exactly 4 years where only two of these four musicians were training under the Gurus.