Ganita Prakash, period by period — fitted to your timetable.

The sequence is not valid. The third child calls out 2, meaning two taller children stand ahead of them. But in a line of four, only two children stand ahead of position 3 (positions 1 and 2). For both of those to be taller than the third child, the third child must be the shortest among the first three. However, the second child calls 0, meaning no one ahead of them is taller, so the second child is taller than the first. That is consistent. The issue is the fourth child calls 1, meaning exactly one of the three ahead is taller. But the third child already called 2 (two taller children in front), so the third child is not the tallest of the first three. The fourth child saying 1 would require exactly one of positions 1, 2, 3 to be taller — this can be consistent. Re-examining: the maximum a child at position k (1-indexed) can call is k – 1. Position 3 can call at most 2, so calling 2 is on the boundary. Position 4 can call at most 3; calling 1 is fine. The sequence 0, 0, 2, 1 requires positions 1 and 2 to both be taller than position 3, yet position 2 calls 0, meaning the first child is not taller than the second. So the second child is taller than or equal to the first. Both being taller than the third is possible. The sequence is actually valid: one valid arrangement is heights 3, 4, 1, 2 — child 1 (height 3) says 0; child 2 (height 4) says 0 (child 1 is not taller); child 3 (height 1) says 2 (both 3 and 4 are taller); child 4 (height 2) says 1 (only height 3 is taller than 2 among 3, 4, 1). The sequence 0, 0, 2, 1 is valid.