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Grades 9-10 Video Solutions 2014
Grades 9-10 Video Solutions 2014 problem1
Grades 9-10 Video Solutions 2014 problem1
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Video Transcription
Q1. The date of the annual kangaroo competition is the 3rd, Thursday and March. What is the earliest possible date of the competition? Obviously, we know that Thursdays occur once a week, so in 14 days, we have exactly 2 Thursdays, that is obvious. And now the question is, what is the minimum number of days we need to fit in 3 Thursdays in that number of days? So suppose that today is Thursday, so we say if Thursday is today, in 14 days, it will also be Thursday. So on the 1st of the month, for example, on the 8th, and also on the 15th, we can have Thursdays. And because increasing the number of days or decreasing the number of days here, if we start on the 2nd, then the 3rd Thursday would be on the 16th, and if we start on the last day of the previous month, we wouldn't have 3 Thursdays. We see that this is the best possible situation, and in 15 days, we can fit 3 Thursdays, so the earliest possible date of the competition has to be the 15th day of the month, so it is the 2nd possibility here, B, 15.
Video Summary
The earliest possible date for the annual kangaroo competition, which falls on the 3rd Thursday of March, is the 15th. Starting from March 1st, Thursdays fall on the 1st, 8th, and 15th. This schedule allows three Thursdays within 15 days. Starting any later will not allow for three Thursdays by the 16th, making March 15th the optimal earliest date.
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