If three coins turn up, two coins at a time, can all three coins turn down? The solution is to calculate parity, and every coin will be turned upside down if it is odd. All coins

Use 0 and 1 to represent the two sides of a coin. Originally, it was 0,0,0 (sum is 0, even number), but it will be changed to 1, 1, 1 (sum is 3, odd number).

Because you have to change two coins at a time, the sum of three coins can only be 2 (two zeros become 1), 0( 1 becomes 0, one zero becomes 1), or -2 (two 1 becomes 0), that is, the change value is even.

Obviously, 0 cannot get 3 by adding or subtracting n even numbers.

Therefore, it proved to be successful.