Ten pieces and the black impossible

Numerical territoryLevel 1 · Starter · ●○○○○

You start with 10 white chips on the table.
In each movement you are obliged to:

choose exactly two tiles,
and flip them (white to black, black to white).

Question: can you end up with exactly one black tile?

Clarification of the statement: you can repeat movements as many times as you want, but always turning over 2 pieces per turn.

Solve this riddle

Hints

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That contradicts the parity invariant.
Reusable idea: When an operation alters quantities 2 at a time, check invariant modulo 2 before attempting long sequences.
Each move changes the number of black pieces by -2, 0 or +2.

Solution

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Back to the problem
Answer: No, it is impossible.
Each move changes the number of black pieces in $-2$, $0$ or $+2$. Therefore, the parity (even/odd) of the number of black pieces never changes.

You start with 0 black (even).
You want to end with 1 quarter note (odd).

That contradicts the parity invariant.
Reusable idea: When an operation alters quantities 2 at a time, check invariant modulo 2 before attempting long sequences.

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