In the 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:
- 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.
- The throws in the last round by both Jakub Vadlejch and Vitezlav Vesely were fouls and were not considered for scoring.
- After four rounds, Vitezlav Vesely was in the second position and could not improve upon his best throw in the succeeding rounds.
- 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?
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Answer: A
Let represent the throw of athlete in round , and represent the best throw of athlete up to round .
We can determine Vitezlav Vesely's (VV) best throw using the following steps:
- Rounds 1 and 2: Clue (i) states that neither VV nor Jakub Vadlejch (JV) had their medal-winning (best) throws in these rounds.
- Rounds 5 and 6: Clue (iii) states that VV could not improve his best throw after round 4, and Clue (ii) states round 6 was a foul. Thus, VV's overall best throw must have occurred in either Round 3 or Round 4, meaning:
- Analyzing Round 4:
- Clue (iii) states that after four rounds, VV was in second position (ahead of JV), which means:
- Clue (iv) states that JV had the best throw in round 4, which means:
- Since , we combine these inequalities:
Since VV's best throw up to round 4 is strictly greater than his round 4 throw, his best throw must have occurred in the Third round.
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