Signal Processing Basics
You cannot calculate all of the solutions because there are an infinite number of solutions. 

If \$F_S\$ is the sampling frequency then any frequency \$n F_S \pm F_j\$ where \$j\$ is 1, 2, or 3, and \$n\$ is any integer, will be aliased to a frequency overlapping one of your original signal frequencies (\$F_1\$, \$F_2\$, or \$F_3\$), and so produce the observed results.