# All your last digit are belong to us

Logic Level 1

$\large{\text{1 \square 2 \square 3 \square \ldots \square 100}}$

Each square in the above expression is replaced by either a $$+$$ or a $$\times$$. For each digit $$0,1,2,\ldots,9$$, can it appear as the last digit of the resulting expression?

As an explicit example, replacing everything with $$+$$ gives the result $$1+2+\ldots+100 = 5050$$, so $$0$$ can be the last digit; the question is whether all ten digits can appear by substituting the squares appropriately (of course different substitution for different digits).

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