josefFeb 20, 2017

#MATHSTODON
can anyone help me with this?

let's say you have a rational number n

what's the best way of computing the shortest list of integers whose mean average is n?

the result could be represented as a list (where some numbers are stated multiple times) e.g:
n = 4.75
avg([7, 7, 4, 1]) = 4.75

or as a set of tuples where the second value is the number of times that number occurs, e.g:
n = 4.75
[ {7, 2}, {4, 1}, {1, 1} ]

Show threadyatchi at snouts nowFeb 20, 2017
@jk do you have a rational representation of the number? a/b?
Show threadyatchi at snouts now
@jk in any case, i think you get there by finding the sum and the number of integers that are in the list (and for any given sum you can trivially get a list by adding the right number of zeros. and work from there if you want one of the infinite other possibilities). if a/b is in simplest form then ab is the sum and b is the number of numbers required, because there is no smaller integer a/b can be multiplied by to produce an integer
Feb 20, 2017 at 8:41pmWeb
Show threadjosefFeb 20, 2017
@yatchi thanks this is helpful!
Show threadyatchi at snouts nowFeb 20, 2017
@jk oops i mean a is the sum
Show threadyatchi at snouts nowFeb 20, 2017

@jk so for 4.75 = 19/4 you need four numbers that sum to 19, and there is no way to do it with fewer than four

and then if you want to do it for a real number the problem is then finding a rational representation of it