- 27 Jun '15 20:36 / 1 edit

The pairs you quote are on opposite sides of the street so*Originally posted by Zuggy***The 6 people live at the following numbers: 123, 132, 213, 231, 312, 321. The closest pairs are (123,132) and (312,321), both differ by 9. I guess you could say the closest would be (123,132) assuming 1 is opposite 2, 3 is opposite 4, etc...**

no way of determining closeness and in British English usage

not "neighbours". The answer I was looking for was 213 & 231. - 28 Jun '15 00:40

Is there a way to solve*Originally posted by wolfgang59***The pairs you quote are on opposite sides of the street so**

no way of determining closeness and in British English usage

not "neighbours". The answer I was looking for was 213 & 231.

a + b + c = a*b*c

To arrive definitively at those results? - 02 Jul '15 15:06

one equation with three unknowns is not definitely defined.*Originally posted by joe shmo***Is there a way to solve**

a + b + c = a*b*c

To arrive definitively at those results?

what you can do is to apply some logic on the digits:

* no "0" involved since the product involving zero is zero, but 000 is not a valid three digit number.

* not more than one digit may be 1 since 1*1*n=n but 1+1+n=n+2

from the first two: no digit bigger than 3 since the smallest including 4 is 124 with 1+2+4=7 and 1*2*4=8, the products increase faster than the sums.

so 123 and its permutations are left over 1+2+306 1+2*3=6, all valid solutions are:

123 132 213 231 312 321 as given above.