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?
(In reply to
answer by Dej Mar)
I created a file of all the house numbers from 1 to 999, with the sum of digits to the right of each house number, and then sorted on the sum of digits primary and house number secondary.
A portion of the sorted file:
...
933 15
942 15
951 15
960 15
79 16 This is line 648
88 16
97 16
169 16
178 16
187 16
196 16
259 16
268 16
277 16
286 16
295 16
349 16
358 16
367 16
376 16
385 16
394 16
439 16
448 16
457 16
466 16
475 16
484 16
493 16
529 16
538 16
547 16
556 16
565 16
574 16
583 16
592 16
619 16
628 16
637 16
646 16
655 16 This is the first of the sod=16 items that's higher than 647
664 16
673 16 This is the first that is prime
682 16
691 16 But this is another such prime
709 16 ... and another
718 16
727 16 ... and another
736 16
745 16
754 16
763 16
772 16
781 16
790 16
808 16
817 16
826 16
835 16
844 16
853 16 ... and another
862 16
871 16
880 16
907 16 ... and another
916 16
925 16
934 16
943 16
952 16
961 16
970 16
89 17
98 17
179 17
...
So it would seem the possible numbers are 673, 691, 709, 727, 853 and 907.
I had not noticed how "completely different prime number" could be interpreted to rule out something that shared any digit with the original address such as 709 repeating the 7 from 647.
That was a good spot of that possibility, Dej Mar.
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Posted by Charlie
on 2018-03-22 10:35:55 |
How I went about it.
