Courgette plant - what should I do?

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I planted a courgette plant quite late this year and it is sitting in its pot outside flowering.
Should I bring it inside so that it can finish growing the courgettes? Or will it survive outside? Some of the big leaves are turning a greyish white.

The flowers are very unlikely to get fertilized inside, so I'd leave outside until it dies off.

I would probably give it a go indoors. My outdoor plants have done well this year but are now looking rather feeble and producing very small courgettes.

M dad used to tickle tomato plants with a feather duster to pollinate the flowers!