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no of true statements about 300 concerning disibility

Source: 2021 Dürer Math Competition Finals Day2 E+8 https://artofproblemsolving.com/community/c2749870_

January 9, 2022
number theorydividesdivisible

Problem Statement

Benedek wrote the following 300300 statements on a piece of paper. 2∣1!2 | 1! 3∣1!   3∣2!3 | 1! \,\,\, 3 | 2! 4∣1!   4∣2!   4∣3!4 | 1! \,\,\, 4 | 2! \,\,\, 4 | 3! 5∣1!   5∣2!   5∣3!   5∣4!5 | 1! \,\,\, 5 | 2! \,\,\, 5 | 3! \,\,\, 5 | 4! ...... 24∣1!   24∣2!   24∣3!   24∣4!   ⋅⋅⋅   24∣23!24 | 1! \,\,\, 24 | 2! \,\,\, 24 | 3! \,\,\, 24 | 4! \,\,\, · · · \,\,\, 24 | 23! 25∣1!   25∣2!   25∣3!   25∣4!   ⋅⋅⋅   25∣23!   25∣24!25 | 1! \,\,\, 25 | 2! \,\,\, 25 | 3! \,\,\, 25 | 4! \,\,\, · · · \,\,\, 25 | 23! \,\,\, 25 | 24! How many true statements did Benedek write down? The symbol | denotes divisibility, e.g. 6∣4!6 | 4! means that 66 is a divisor of number 4!4!.
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