Brain Teaser Answer

Fred got rid of seven calendars: 1983, 1986, 1987, 1989, 1990, 1991, and 1993. He needed a total of

fourteen calendars, but it took him seven years to buy the last two: 1996 and 2000.

Luckily for him, Fred has a penchant for esoteric knowledge. He knew that as long as every four years

was a leap year until he died, he could figure out his calendar problems with a few, easy rules:

- If the year is a leap year, he could reuse its calendar in years that were multiples of 28 from that year.

- If the year is the first year after a leap year, he could reuse its calendar in years that were multiples of

6, 17, or 28 from that year.

- If the year is the second year after a leap year, he could reuse its calendar in years that were multiples

of 11, 17, or 28 from that year.

- If the year is the third year after a leap year, he could reuse its calendar in years that were multiples of

11, 22, or 28 from that year.

Since 2100 will not be a leap year, Fred knows that rules will get out of whack if he lives past 124. (He

wasn't too worried about having to spend extra money, though, his family typically only lives to their mid-

to late-nineties.)

Fred was 18 in 1993, so he must have been born in 1975. Since he had a calendar for every year he's

been alive, he started with 19 calendars. He quickly saw that the most calendars he would ever need was

28 since all calendar years repeat after 28 years. He figured that it would be a lot less, though, and, since

he didn't really like math, just drew up a table to help him determine the actual number. The table

consisted of the calendars he would need and what years they would represent.

1975: 1986, 1997, 2003, 2014, 2025, 2031, 2042, 2053, 2059, 2070, 2081, 2087, 2098

1976: 2004, 2032, 2060, 2088

1977: 1983, 1994, 2005, 2011, 2022, 2033, 2039, 2050, 2061, 2067, 2078, 2089, 2095

1978: 1989, 1995, 2006, 2017, 2023, 2034, 2045, 2051, 2062, 2073, 2079, 2090

1979: 1990, 2001, 2007, 2018, 2029, 2035, 2046, 2057, 2063, 2074, 2085, 2091

1980: 2008, 2036, 2064, 2092

1981: 1987, 1998, 2009, 2015, 2026, 2037, 2043, 2054, 2065, 2071, 2082, 2093, 2099

1982: 1993, 1999, 2010, 2021, 2027, 2038, 2049, 2055, 2066, 2077, 2083, 2094

1984: 2012, 2040, 2068, 2096

1985: 1991, 2002, 2013, 2019, 2030, 2041, 2047, 2058, 2069, 2075, 2086, 2097

1988: 2016, 2044, 2072

1992: 2020, 2048, 2076

1996: 2024, 2052, 2080

2000: 2028, 2056, 2084

It didn't take him too long to come up with, and at the end he had a useful resource that he could keep

with his calendars. Using the table he had created, he would know which one to break out at the start of

a new year.