Flop game: In a math class, the teacher numbered 54 playing cards in the order of 1, 2, 3, …, 54, and arranged them in a row with their backs up.

A * * * There are seven playing cards with faces up, numbered 1, 4,9,16,25,36,49.

Reason: Whether the playing cards are turned over in the end mainly depends on how many times they are turned over.

If you flip through it several times, it's still the same as before.

If you turn it over an odd number of times, it will end up upside down.

Whether the number plate N can be turned over or not depends on whether the number of factors of the number N is odd or even (including 1 and itself).

For example, 1 has only one factor, 1,

2 has two factors 1, 2,

3 has two factors 1, 3,

4 has three factors: 1, 2, 4, … It is not difficult to judge.

Every square number has an odd number of factors,

Thus, the playing cards numbered 1, 4, 9, 16, 25, 36, 49 were finally turned upside down.