Demonstration that least squares give maximum likelihood

I'm an analytical chemist, not terribly at ease with statistics. For teaching purposes I'd like to get a better feel for the subject, but have given up hope of mastering the abstract maths. Information available on the web tends to go over my head (a comment that has been made by contributors to Wikipedia).

So, I'd like to ask if anyone knows of a straightforward didactic demonstration from first principles (for example coin tossing experiments) that the most probable result for unbiased repeated measurements on identical samples is obtained by minimising the sum of the experimental errors squared?

In practice, the errors are unknowable so we use residuals. It is nearly always safe to assume normality in this field (the data, not necessarily the chemists).

Regards

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