Sum or difference can get 0 ?

Number Theory Level 3

1 + 2 − 3 = 0 1 − 2 − 3 + 4 = 0 1 + 2 − 3 + 4 − 5 − 6 + 7 = 0 \small \begin{aligned}& 1 +2 -3 = 0 \\& 1 -2 -3 +4 =0 \\& 1+2-3+4-5-6+7 =0 \end{aligned} Is it possible to make the equation below true using suitable operators ( + , − ) (+ , - ) ?

1 2 3 ⋯ ⋯ 2018 = 0 \small\begin{aligned} 1 \quad 2 \quad 3 \quad \cdots\cdots \quad 2018 =0 \end{aligned}

No Yes

Naren Bhandari by Naren Bhandari , 21, India

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1 solution

There are an odd number of odd numbers in this sum, guaranteeing an odd answer but 0 is even so this is impossible.

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