[Guest]

When Mr. Albright queried Mr. Brennan about his year of birth, Mr. Brennan replied, "My year of birth is a 4-digit year which is the only prime number in its decade, such that this decade which is in the 20th Century contains no numbers divisible by 13."

Can you assist Mr. Albright in deducing Mr. Brennans birth year from the above statement?

Edited January 8, 2010 by K Sengupta

[Guest]

1987

The number is prime of the form 19XY

Here are all such primes:

1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999

We eliminate all primes falling in the same decade, which leaves

1913, 1949, 1951, and 1987

Of these we search for a substring whose numerical value is a multiple of 13 and eliminate it.

1913 obviously contains 13.

1949 contains 949 which is 13*73.

1951 contains 195 which is 13*15.

This leaves 1987.

[preflop]

When Mr. Albright queried Mr. Brennan about his year of birth, Mr. Brennan replied, "My year of birth is a 4-digit year which is the only prime number in its decade, such that this decade which is in the 20th Century contains no numbers divisible by 13."

Can you assist Mr. Albright in deducing Mr. Brennan’s birth year from the above statement?

1949

only 1900s, 1940s, and 1990s have no years divisible by 13 in the 20th century.

of those 1900s has two primes 1901 & 1907

1990s has three primes 1993, 1997, 1999.

This leaves us with the 1940s which has only one prime 1949.

[Guest]

1949

only 1900s, 1940s, and 1990s have no years divisible by 13 in the 20th century.

of those 1900s has two primes 1901 & 1907

1990s has three primes 1993, 1997, 1999.

This leaves us with the 1940s which has only one prime 1949.

Haha, I misread and misunderstood the original posting.

Good job

I'm amazed I found exactly one solution to the problem I thought he was asking

Edited January 9, 2010 by mmiguel1

[Guest]

Answer is 1949

[Guest]

relevant prime numbers:

1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999

relevant multiple of 13 :

1911 1924 1937 1950 1963 1974 1987

Answer:1949

[Guest]

relevant prime numbers:

1901 1907 1913 1931 1933 1949 1951 1973 1979 1987 1993 1997 1999

relevant multiple of 13 :

1911 1924 1937 1950 1963 1974 1987

Answer:1949

How did you divide 1987 by 13?