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Let ai represent the number of hours spent by the child watching Tv within the first i days.
Taking 11 hours = one week, then for seven weeks is ( 11 * 7) = 77 hours'
Then 0 < a1 < a2 < < a49 < 77
Since each of the seven weeks the child watches Tv at most 11 hours.
Also, all numbers in the sequence a1 + 20, a2 + 20, , a49 + 20 are distinct and none of them exceeds 97.
But in the two sequences together, there are 98 numbers.
Thus it follows that from day ( j + 1) to day i, the child watches Tv for exactly 20 hours.