Three small smooth spheres \(A\), \(B\) and \(C\) of masses \(0.2 \text{kg}\), \(0.7 \text{kg}\) and \(m \text{kg}\) respectively are free to move in a straight line on a smooth horizontal table. Initially \(B\) and \(C\) are stationary and \(A\) is moving with velocity \(1.8 \text{ms} ^{-1}\) directly towards \(B\). The coefficient of restitution for the collision between \(A\) and \(B\) is \(e\). Immediately after this collision the speed of \(A\) is greater than the speed of \(B\).

\((\text{i})\) Calculate the set of possible values of \(e\).

It is now given that the speed of \(B\) immediately after the collision with \(A\) is \(0.75 \text{ms} ^{−1}\). \(B\) continues its motion and strikes \(C\) directly in a perfectly elastic collision. \(B\) has speed \(0.25 \text{ms} ^{−1}\) immediately after its collision with \(C\).

\((\text{ii})\) Calculate the two possible values of \(m\).

**Input the sum of the two possible values of \(m\) as your answer.**

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