Solution
79 mangos

Xpress-Mosel Model

model 'mango'

! Description  : Mango puzzle
! Source       : M Kraitchik - Mathematical Recreations (P32)
! Date written : MAGIC 19/11/92, Xpress-MP 22/6/98, Mosel 17/4/03
! Written by   : M J Chlond

  uses 'mmxprs'

  declarations
    x: array(1..5) of mpvar
  end-declarations


  minval:= x(5)

  take1:= -3*x(1)+x(2) = 1 
  take2:= -1.5*x(2)+x(3) = 1
  take3:= -1.5*x(3)+x(4) = 1
  take4:= -1.5*x(4)+x(5) = 1

  forall(i in 1..5)
    x(i) is_integer
  
  minimise(minval)
  
  forall(i in 1..5)
    write(getsol(x(i)),' ')
    
end-model