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Monday, March 24, 2008

How Old is she Now?

Nine years ago Karen was in her prime, eight years ago she was a power of a prime, and last year Karen was really odd.

How old is Karen now?


Joel said...

Karen is 12

9 years ago was 3 (PRIME)

8 years ago was 4 (square of 2 (PRIME))

Last year was really odd (11 is odd - and also PRIME)

Ginkgo100 said...

I started getting into the hundreds... realized Karen was probably not that old... then figured out what Joel said. Yeah, two and three are both prime -- duh.

Anonymous said...

16-8=8 (2^3)

Erik said...

There are 3, maybe 4, possible solutions to this problem. To find all the possible solutions first find all powers of primes that are less than a reasonable age for a human (roughly 120 years), then compare that list with a list of primes in the same range.

Powers of primes are:
2^2 = 4
2^3 = 8
3^2 = 9
2^4 = 16
5^2 = 25
3^3 = 27
2^5 = 32
7^2 = 49
2^6 = 64
11^2 = 121
2^7 = 128

Compare these values with the list of primes and eliminate all powers of primes that are not 1 larger than a prime. This leaves only these values:
4 (3 is prime)
8 (7 is prime)
32 (31 is prime)
128 (127 is prime)

Add 8 to any of these powers of prime values to find the age that Karen COULD be. Joel found '12', and anonymous provided '16'. Karen could also be 40, and as a stretch, Karen COULD be 136 but that's not likely since the oldest verified age of any human has been "only" 122.