# Neighbours 2

wolfgang59
Posers and Puzzles 25 Aug '15 22:22
1. wolfgang59
howling mad
25 Aug '15 22:22
So little action on this forum I've contrived this little puzzle.

Five couples live on the same street, they are amazed to discover that the reciprocals of their house numbers when summed is equal to 1.

Furthermore when one of the couples gets divorced and they sell their property to buy two houses the reciprocals of all 6 houses sums to 1.

At what number did the divorced couple live at?

(Probably multiple solutions ... I have the easy one!)

ðŸ˜€
2. Ponderable
chemist
26 Aug '15 12:56
I wrote a lengthy bit on how to obtain the numbers, but I leave you with the solution only:

5 houses: 2,3,12,18,36

6 houses: 2,6,9,12,18,36
3. Ponderable
chemist
26 Aug '15 14:36
Originally posted by Ponderable
I wrote a lengthy bit on how to obtain the numbers, but I leave you with the solution only:

5 houses: 2,3,12,18,36

6 houses: 2,6,9,12,18,36
The former post was wrong...

I think there are a lot of solutions, lets try for a few:

5 pairs: 2,4,9,12,18
6 pairs: 3,4,6,9,12,18 (splitting the 1/2 into 1/3 + 1/6)

5 pairs: 3,4,5,6,20
6 pairs: 3,4,5,9,18,20 (splitting the 1/6 into 1/9+1/18)

5 pairs: 2,4,9,12,18
6 pairs: 2,5,9,12,18,20 (splitting the 1/4 into 1/5 and 1/20)

5 pairs: 2,4,9,12,18
6 pairs: 3,4,6,9,12,18

5 pairs: 2,4,9,12,18
6 pairs: 2,4,9,16,18,48

...and so on
4. wolfgang59
howling mad
26 Aug '15 23:57
Originally posted by Ponderable

I think there are a lot of solutions, lets try for a few:

5 pairs: 2,4,9,12,18
6 pairs: 3,4,6,9,12,18 (splitting the 1/2 into 1/3 + 1/6)

...and so on
Good enough.