math.questions.4469824.name-for-addition-and-multiplication-of-a-sequence-of-digits-using-varying-order.md

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Name for addition and multiplication of a sequence of digits, using varying order of mathematical symbols, with the same outcome

I am looking for the correct name for mathematics like this:

$1 + 2 \times 3 + 4 \times 5 + 6 \times 7 + 8 = 77$

$1 + 2 + 3 + 4 + 5 + 6 + 7 \times 8 = 77$

$1 \times 2 \times 3 + 4 + 5 + 6 + 7 \times 8 = 77$

That is to say: maths that uses the same digits, in sequence, but with varying mathematical symbols, in order to reach the same integer.

For clarification:

• The sum doesn't need to be 77, that just an example.
• Only addition and multiplication are used¹
• It could be less digits (e.g. just using 1, 2, 3, and 4)
• It could be all digits (i.e. 1, 2, 3, 4, 5, 6, 7, 8, 9)²

Anyway, I'd like to learn/read more about things like this, but I have no idea what to look for.

So... How are these kind of calculations called?

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Until a name for these equations comes to light, I will name them after myself:

Peachey Equations

To calculate them, I have created the Peachey Equation Generator

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¹ if there is a term, but only if division and subtraction are included, then that's okay too...

² Not sure if/where zero fits in here...