(;) Semicolon Math: Number of distinct y-coordinates

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Number of distinct y-coordinates (ID: 18)

Problem status: not solved

Let \(A_1 = (0,0), A_2=(1,0), A_3=(2,0), A_4=(3,0),A_5=(4,0)\) and \(B_1 = (0,1), B_2=(1,1), B_3=(2,1), B_4=(3,1),B_5=(4,1).\) Let \(L\) be the set of line segments \(A_iB_j\) where \(i\) and \(j\) are integers with \(1 \le i, j \le 5.\) (\(i\) and \(j\) do not need to be distinct.) Let \(S\) be the set of points in the interior of rectangle \(A_1A_5B_5B_1\) that are the intersection of two distinct line segments in \(L.\)

Of all the points in \(S,\) how many different \(y\)-coordinates are there? If two points have the same \(y\)-coordinate, then that \(y\)-coordinate should only be counted once.

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