Part Number For Starter Solenoid  Simplicity Regent 17HP 31F777 engine 

Solenoid Kit 1686981YP

 
https://www.ereplacementparts.com/solenoid-kit-p-1685653.html 
 
 
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Cheers mate this is mine it looks like 3 point what you think

I'm not sure what you mean and no pic posted...
 
FYI, for the separate solenoid, there are 2 styles:
            (1) There's four connectors.  The two small ones are for ground and for the trigger.
           
            (2) There's 3 connectors.  the small one is the trigger wire, the ground is
                     completed when you bolt it down to the metal frame/engine etc
                         (no need for another/separate ground)
 
 
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does it matter which one you have or not 

Nope, not at all.  Just two different styles...