The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?

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?

Answer 1

A different way to reach the same answer is to walk through the calendar month by month instead of jumping straight to a 31 day gap.

Days left in June: June has 30 days total, and we start counting from June 2 (a Thursday). The days remaining in June after June 2 run from June 3 up to June 30, which is $30-2=28$ days.
Add the days into July: after reaching the end of June, we still need to move 3 more days into July to land on July 3. So the total number of days moved forward is $28+3=31$ days.
Reduce using full weeks: $28$ of those $31$ days make exactly $4$ full weeks ($28 = 4\times7$), which brings the day of the week right back to Thursday. The leftover $31-28=3$ days then shift the day forward by 3 more steps.
Step through the leftover days: Thursday, then 1 day later Friday, then 2 days later Saturday, then 3 days later Sunday.

Both ways of counting agree: July 3 lands 3 weekdays after Thursday, which is Sunday.

Let's summarize:

June has 30 days, so June 2 to July 2 is a 30 day gap, and June 2 to July 3 is a 31 day gap.
Every full block of 7 days brings the weekday back to where it started.
Only the remainder after removing full weeks (here, 3 days) decides the final shift from Thursday.

So July 3 falls on a Sunday.

Answer 2

A different way to reach the same answer is to walk through the calendar month by month instead of jumping straight to a 31 day gap.

Days left in June: June has 30 days total, and we start counting from June 2 (a Thursday). The days remaining in June after June 2 run from June 3 up to June 30, which is $30-2=28$ days.
Add the days into July: after reaching the end of June, we still need to move 3 more days into July to land on July 3. So the total number of days moved forward is $28+3=31$ days.
Reduce using full weeks: $28$ of those $31$ days make exactly $4$ full weeks ($28 = 4\times7$), which brings the day of the week right back to Thursday. The leftover $31-28=3$ days then shift the day forward by 3 more steps.
Step through the leftover days: Thursday, then 1 day later Friday, then 2 days later Saturday, then 3 days later Sunday.

Both ways of counting agree: July 3 lands 3 weekdays after Thursday, which is Sunday.

Let's summarize:

June has 30 days, so June 2 to July 2 is a 30 day gap, and June 2 to July 3 is a 31 day gap.
Every full block of 7 days brings the weekday back to where it started.
Only the remainder after removing full weeks (here, 3 days) decides the final shift from Thursday.

So July 3 falls on a Sunday.

The 2nd of June is a Thursday in a certain year. Which day of the week is the 3rd of July in that year?

Show Hint

The Correct Option is D

Solution and Explanation

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