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Originally posted by ZuggyThe pairs you quote are on opposite sides of the street so
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.
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Originally posted by wolfgang59Is there a way to solve
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?
Originally posted by joe shmoone equation with three unknowns is not definitely defined.
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.