jasen 4 Posted July 15, 2016 Report Share Posted July 15, 2016 We are 3 sisters, today our ages are primes, interestingly the difference of our ages are also primes. How old we are ? Quote Link to post Share on other sites

0 Solution sushma 0 Posted July 15, 2016 Solution Report Share Posted July 15, 2016 2 5 and 7 Quote Link to post Share on other sites

1 DejMar 9 Posted July 15, 2016 Report Share Posted July 15, 2016 (edited) Spoiler Given that the ages are primes, at least two of the ages must be odd. The difference of any two odd numbers must be even, and as the difference is given to be prime that difference must be 2 -- the only even prime. As the ages must be different (as zero is not prime), it can be deduced that one and only one of the ages must be even, id est 2. The set of ages must then be {2, p, p+2}, such that p is a prime and p-2 and p+2 are also prime. This only occurs where p is equal to 5: (p-2) = 3 & (p+2) = 7. It therefore can be declared the set of ages is {2, 5, 7}. Edited July 15, 2016 by DejMar type Quote Link to post Share on other sites

0 telesphorelalancette 0 Posted August 11, 2016 Report Share Posted August 11, 2016 They could be 1, 3 and 5 or 7, 9 and 11. Nice one Jasen! Quote Link to post Share on other sites

0 jasen 4 Posted August 17, 2016 Author Report Share Posted August 17, 2016 Just now, telesphorelalancette said: They could be 1, 3 and 5 or 7, 9 and 11. Nice one Jasen! wrong Spoiler only 1 answer, 2,5, 7 no more 5 - 1 = 4, not prime 11 - 7 = 4, not prime Quote Link to post Share on other sites

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## jasen 4

We are 3 sisters,

today our ages are primes,

interestingly the difference of our ages are also primes.

How old we are ?

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