Question

In the 2020 summer Olympics’ Javelin throw finals, Neeraj Chopra exhibited a
spectacular performance to win the gold medal. The silver medal was won by
Jakub Vadlejch and the bronze medal was won by Vitezlav Vesely. There were
six rounds of throws with each athlete having one throw per round. The best of
all the throws of each athlete is considered for the medal. Following were the
observations about the throws:
i.
The first and second rounds were dominated by Neeraj Chopra with a gold
medal performance in his second throw, while the other two athletes did
not have any medal winning throws in these rounds.
ii.
The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely
were fouls and were not considered for scoring.
iii.
After four rounds, Vitezlav Vesely was in the second position and could
not improve upon his best throw in the succeeding rounds.
iv.
In the fourth round, the throw by Jakub Vadlejch was the best in that
round.
In which round did Vitezlav Vesely have his best throw?

• A. Third
• B. Fourth
• C. Fifth
• D. Sixth

Hint:

Eliminate rounds 1, 2 (Neeraj's story), 6 (fouls), and 5 (no improvement after round 4) first; then show round 4 is impossible because it would force Jakub's best to exceed Vitezlav's, contradicting Vitezlav being ranked ahead of Jakub after 4 rounds - leaving round 3.

Answer 1

The Correct Option is A

Step 1: Set up the framework. Three athletes - Neeraj Chopra (gold), Jakub Vadlejch (silver), Vitezlav Vesely (bronze) - each get one throw per round across 6 rounds. Each athlete's medal position is decided by their single best throw across all 6 rounds. We must find the round in which Vitezlav Vesely recorded his personal best throw.

Step 2: Use clue (i). Neeraj's gold-medal-winning throw (his personal best) occurred in round 2. Also, neither Jakub nor Vitezlav had a "medal winning" throw (i.e., their personal-best throw) in rounds 1 or 2. So Vitezlav's best throw is not in round 1 or round 2.

Step 3: Use clue (ii). In round 6, both Jakub's and Vitezlav's throws were fouls (not counted at all). So Vitezlav's best throw is not in round 6.

Step 4: Use clue (iii). After 4 rounds, Vitezlav was in second position (ahead of Jakub, behind Neeraj) and did not improve his best throw in rounds 5 or 6. This tells us two things: (a) Vitezlav's personal-best throw must have already occurred within rounds 1-4 (since he never beats it afterward), and (b) after 4 rounds, Vitezlav's best-so-far exceeds Jakub's best-so-far.

Combining Steps 2-4: Vitezlav's best throw occurred in round 3 or round 4.

Step 5: Use clue (iv) to break the tie. In round 4, Jakub's throw was the best among all three athletes' throws in that specific round. Suppose, for contradiction, that Vitezlav's personal best occurred in round 4 itself. Then Jakub's round-4 throw would have to be even farther than Vitezlav's round-4 throw (since Jakub's round-4 throw was the best of that round). That would make Jakub's best-so-far (after 4 rounds) at least as large as his round-4 throw, which is larger than Vitezlav's round-4 throw - which we assumed was Vitezlav's personal best. This would mean Jakub's best-so-far exceeds Vitezlav's best-so-far after 4 rounds, contradicting clue (iii), which places Vitezlav ahead of Jakub after 4 rounds.

Step 6: Conclude. Since round 4 leads to a contradiction, Vitezlav's personal best throw must have occurred in round 3.

\[ \text{Vitezlav Vesely's best throw was in the Third round.} \]

Final Answer: (A) Third