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Zorluk: OrtaClocks and Calendars

An international exhibition is inaugurated on January 26th of a leap year, which falls on a Thursday. The closing ceremony is scheduled for October 15th of the same year. On what day of the week will the closing ceremony take place?

Cevap: Monday / monday

Cevap

Monday
The total number of days elapsed from January 26th to October 15th in a leap year is exactly 263263 days. Dividing 263263 by 77 gives 3737 full weeks and a remainder of 44 odd days. Counting 44 days forward from Thursday results in Monday.

Adım Adım Çözüm

1
Calculate the remaining days in January and note the full days in the intervening months.
January: 55 days (31−2631 - 26). February: 2929 days (since it is a leap year). March: 3131, April: 3030, May: 3131, June: 3030, July: 3131, August: 3131, September: 3030.
To find the total number of days elapsed between January 26th and October 15th, we must sum the relevant days in each month.
2
Add the days of the final month (October) to the sum of the previous months.
5+29+31+30+31+30+31+31+30+15=2635 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 15 = 263 days.
This calculation yields the exact number of days that pass from the inauguration to the closing ceremony.
3
Divide the total number of elapsed days by 77 to find the remainder (odd days).
263÷7=37263 \div 7 = 37 with a remainder of 44 days.
Since the days of the week repeat every 77 days, only the remainder affects the final day of the week.
4
Count 44 days forward from the starting day (Thursday).
Thursday +1=+ 1 = Friday, +2=+ 2 = Saturday, +3=+ 3 = Sunday, +4=+ 4 = Monday.
Adding the odd days to the initial day correctly determines the final day of the week.

Anahtar Kavram

Calculating elapsed days across multiple months and using the concept of odd days (modulo 7 arithmetic) to determine the exact day of the week.
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Clocks and Calendars

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