My sister Mathy used to live at Holm East St., a long street with 999 door numbers. When I tell her that I want to visit her, she said:

- OK. But remember that I have moved. I am not anymore at number 647 but I have moved ahead, in the same street, to a completely different prime number.

- What is it?, I asked.

- Oh!, you should guess it, she said. If you sum the digits of my new number it happens that there are just 647 doors with an inferior sum.

So, where does she live now?

There are 647 numbers of the set of numbers between 001 and 999 where the digital sum is less than 16. Thus, the digital sum of the
number Mathy had moved is given to equal to 16.
With the given that Mathy moved "ahead" from 647 to a another prime, there are six primes that are greater than 647 and have a digital sum of 16. These primes are: 673, 691, 709, 727, 853, 907.
Mathy's comment that the prime is completely different can be interpreted in assumption to mean that the digits of the new number are not shared with that of her old door number of 647. With this assumption, there is but one door number for where she would now be residing. Mathy now lives at the house with door number 853.

Posted by Dej Mar on 2018-03-22 09:30:57