Pulley and Block system

In the arrangement shown in the figure, the pulleys are massless and frictionless and the threads are inextensible.

The block with mass m 1 m_1 will remain at rest if __________ . \text{\_\_\_\_\_\_\_\_\_\_}.

m 1 = m 2 + m 3 m_1=m_2+m_3 1 m 1 = 1 m 2 + 1 m 3 \frac{1}{m_1}=\frac{1}{m_2}+\frac{1}{m_3} 4 m 1 = 1 m 2 + 1 m 3 \frac{4}{m_1} = \frac{1}{m_2}+ \frac{1}{m_3} 1 m 3 = 2 m 2 + 3 m 1 \frac{1}{m_3}=\frac{2}{m_2}+\frac{3}{m_1}

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