Open interest accounting

A new futures contract trades for three days among traders A–E. Day 1 (price 100 → 102): A buys 10 from B; both open. Day 2 (102 → 101): C buys 6 from A (A is closing); D buys 4 from E (both open). Day 3 (101 → 103): B buys 6 from C (both closing); E buys 4 from A (both closing). (a) Compute each day's volume, OI and $\Delta$OI, and verify the identity $\Delta\text{OI} = N_{oo} - N_{cc}$. (b) List each trader's position at the end of each day. (c) Apply the broker labels from 7.5 to each day. For day 3, explain why "short covering" is at best half the story.