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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584

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BuyFindarrow_forward

Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
ISBN: 9781305965584
Textbook Problem

Many people consider the 13th of the month an unlucky day when it falls on a Friday.

a. Does every year have a Friday the 13th? Explain why or why not.

b. What is the greatest number of Friday the l3ths that can occur in one year? Can you find a recent year in which this number occurred? Hint: A non-leap year can have two consecutive months where the 13th is a Friday.

a.

To determine

To calculate: To explain does every year have a Friday the 13th

Explanation

Given information: 13th of the month an unlucky day when it falls on a Friday

Calculation:

Consider a regular non-leap year

Suppose that January begins on day  k , (with means Sunday), then

1. January begins on day  k ;

2. February begins on day since January has 31 days, and

3. March begins on day

4. April begins on day

5. May begins on day (since April has 30 days, and

6. June begins on day

7. July begins on day

8. August begins on day k+9k+2mod7 ;

9. September begins on day k+5mod7 ;

With these, there are already days  k,k+1,k+2,k+3,k+4,k+5 and k+6 so at least one of these months will begin on Sunday, guaranteeing at least one Friday 13th

b.

To determine

To calculate: To find the greatest number of Friday the 13ths that can occur in one year, and to find a recent year I which this number occurred

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