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:

First narrow VV's best throw down to round 3 or round 4 using the medal and foul clues, then use the round 4 comparison with Jakub Vadlejch to see which one is actually possible.

Answer 1

The Correct Option is A

Step 1: List what each clue rules out for Vitezlav Vesely (VV).
Clue (i) says the first and second rounds belonged to Neeraj Chopra, and that neither Jakub Vadlejch (JV) nor VV had a medal winning throw in those two rounds. So VV's best throw is not in round 1 or round 2.

Step 2: Use clue (ii) to remove round six.
Clue (ii) says VV's throw in round six was a foul and was not scored. A foul cannot be anyone's best throw, so VV's best throw is not in round 6.

Step 3: Use clue (iii) to remove rounds five and six.
Clue (iii) says that after four rounds VV was in second position and could not improve on his best throw in the rounds that followed. This means VV's overall best throw was already set within the first four rounds, so it cannot be round 5 (round 6 is already ruled out anyway). Combining this with Step 1, VV's best throw must be round 3 or round 4.

Step 4: Use clue (iv) to test round four for VV.
Clue (iv) says that in round four, JV's throw was the best among the three throws in that round, which means JV's round 4 throw was bigger than VV's round 4 throw. Suppose VV's best throw actually happened in round 4. Then VV's best so far after four rounds would equal his round 4 throw. But JV's best so far after four rounds is at least as big as JV's round 4 throw, which is bigger than VV's round 4 throw. That would make JV's best so far bigger than VV's best so far after four rounds, putting JV ahead of VV.

Step 5: Compare with clue (iii) again.
Clue (iii) clearly states VV was in second position, ahead of JV, after four rounds. This directly contradicts what Step 4 would give if VV's best throw were in round 4. So round 4 cannot be VV's best throw.

Step 6: Conclude by elimination.
Rounds 1, 2, 5 and 6 are ruled out by Steps 1 to 3, and round 4 is ruled out by Steps 4 and 5. The only round left is round 3.

Final Answer:
Vitezlav Vesely had his best throw in the third round. \[ \boxed{\text{Third}} \]