in High School Math

Calendar Problem: Calculate Day of Week from Date

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Calculating the Day of the Week

Have you ever wondered how to quickly figure out the day of the week for any given date? There’s a neat mathematical trick that can help you do just that! This technique is often featured in mental math competitions, and it’s surprisingly simple once you get the hang of it.

The Algorithm

Here’s how the algorithm works:

  1. Assign values to the months:
    • January: 1
    • February: 4
    • March: 4
    • April: 0
    • May: 2
    • June: 5
    • July: 0
    • August: 3
    • September: 6
    • October: 1
    • November: 4
    • December: 6
  2. Adjust for leap years: If the year is a leap year and the month is January or February, subtract 1 from the month value.
  3. Calculate the century code: Divide the century by 4, discard the remainder, and multiply the result by 2. Then, add the remainder from the original division by 4.
  4. Calculate the year code: Take the last two digits of the year, divide by 4, discard the remainder, and add the result to the last two digits of the year.
  5. Add all the values: Add the month value, the day of the month, the century code, and the year code.
  6. Divide by 7: Divide the sum by 7 and take the remainder.
  7. Interpret the remainder:
    • 0: Saturday
    • 1: Sunday
    • 2: Monday
    • 3: Tuesday
    • 4: Wednesday
    • 5: Thursday
    • 6: Friday

Example

Let’s find the day of the week for July 4, 2024:

  1. Month value: July = 0
  2. Leap year adjustment: None needed since July is not in January or February.
  3. Century code: 20 / 4 = 5 (discard remainder), 5 * 2 = 10. The remainder from 20 / 4 is 0, so the century code is 10 + 0 = 10.
  4. Year code: 24 / 4 = 6 (discard remainder), 6 + 24 = 30.
  5. Sum: 0 + 4 + 10 + 30 = 44
  6. Divide by 7: 44 / 7 = 6 remainder 2
  7. Day of the week: A remainder of 2 corresponds to Monday. Therefore, July 4, 2024, falls on a Monday.

Practice Makes Perfect

This algorithm might seem a bit complicated at first, but with practice, you’ll be able to calculate the day of the week for any date in no time. Try it out with different dates and see how quickly you can master this mental math trick!

Problem solving