yeah! You are right Q&A section.
It is an interesting problem and would be better if put in Q&A section as there is only one possible solution as under:
100 ohm -> using single resistor, not putting other two in circuit
200 ohm -> using 2 resitors in series, not putting the third in circuit
300 ohm -> using all 3 in series
50 ohm -> using 2 resistors in parallel, not putting the third in circuit
150 ohm -> using one resistor put in series with the other two put in parallel
66.7 ohm -> using one resistor put in parallel with the other two put in series
It uses the basic principle of addition of resistances in series and parallel.
Asuming R1, R2, R3, ---- are the given resistances of the resistors and R is the resultant resistance of the combination then:
In a series circuit, R = R1 + R2 + R3 + ----
In a parallel circuit 1/R = 1/R1 + 1/R2 + 1/R3 + ----
In a combination circuit, where both parallel and series circuits are used, we calculate the combined resistance of the sub-circuits (series or parallel) using the above addition rules till the whole circuit is resolved to a single type (series or parallel.