# 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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