At the end of the previous month the total age of the group is 37n.
This month (before the change in memberships) the average age is 37+1/12 and the total age is (445/12)n since everyone got a month older.
After adding and subtracting members the total age increases by 111-m and there are n+2 members so the new average is
Since they are 18 months lower (than which? I've assumed than last month)
[(445/12)n+111-m]/(n+2) = 37-1.5 = 71/2
Which doesn't seem to have any values where both are squares. n=55^2, m=1113^2 is close but that person who left is over a million years old.
Posted by Jer
on 2013-04-29 14:04:46