Are three SPST switches required to convert two resistors from being in series to being parallel
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The simplest arrangement is with a DPDT switch.

Since you seem to be constrained to using SPST switches you will need as many switches as there are contacts in use on the DPDT switch in Figure 1. That's two wired as NC (normally closed) and one NO (normally open) using the reference positions shown in the schematic.


  Are three SPST switches required to convert two resistors from being in series to being parallel?


Yes.

Be very aware - particularly if using high currents or voltages - that replacing the bottom changeover contact with two SPST switches gives you the ability to short out V1 and V2. You would probably need to mechanically tie the levers together to ensure actuation of all three switches simultaneously.



Update after comment in OP

I have two water filters that I need to be able to place in parallel or series.

This is a bit different than your original post suggested. The filters have a directional constraint otherwise you will wash the filtered material out of the filter when you reverse the flow. As a result your electrical analogy requires diodes, not resistors. Also a current source seems more appropriate!







simulate this circuit

*Figure 2: (a) If you could find a 3-port valve you could achieve your aim with two valves. Otherwise three 2-port valves are required. (b) Parallel mode. (c) Series mode.







simulate this circuit

Figure 3. The valve count can be reduced to two with the addition of a non-return or "check" valve. If this is of the spring type there will be a drop in pressure across it. In parallel mode it will be closed.


  I thought that three would be the minimum required, but I was hoping that perhaps there was some tricky configuration that would do it with two.


There you go!