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Distinguishing Ball Colors via Queries

2175ExpertGraph TheoryCombinatorics

Team Selection Test for JBMO 2024 · 2024

There are 207 boxes on the table numbered $1, 2, \ldots, 207$. Asli puts one red ball to each of some 100 boxes and one white ball to each of the remaining 107 boxes. After that Zehra writes $N$ pairs $(i, j)$, $1 \le i < j \le 207$ to the board. Finally for each pair $(i, j)$ on the board Asli informs Zehra whether balls in the boxes $i$ and $j$ are same-coloured. Find the minimal value of $N$ for which Zehra can guarantee to determine the colours of balls in all boxes.
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