Please read this first.

Yet there is a failsafe strategy without pre-agreed answers.

Here goes:

Time for our next million dollar question! Is it possible for the x and y components of the spins of the three particles to be in possession of values even if no values are actually measured?

Caustic Sea (detail) by Eric J. Heller.

Right, the answer is again negative. For the same reason that there can be no strategy with pre-agreed answers, there can be no pre-existent values.

To check this, let us assume — contrary to the facts — that spin components have values irrespective of what is and what is not measured. And suppose that the y components of the three spins have been measured, and that the following values were obtained: Y_A, Y_B, Y_C. (These expressions now stand for specific values, either +1 or –1.)

Since the product X_A Y_B Y_C is sure to come out equal to 1, we are entitled to conclude that if we had measured X_A instead of Y_A, we would have obtained X_A= (Y_B Y_C)^–1.

By the same token we are entitled to conclude that if we had measured X_B instead of Y_B, we would have obtained X_B= (Y_A Y_C)^–1, and that if we had measured X_C instead of Y_C, we would have obtained X_C= (Y_A Y_B)^–1.

Ergo, if we had measured all three x components instead of the three y components, the product of the outcomes would have been

(Y_B Y_C)^–1 (Y_A Y_C)^–1 (Y_A Y_B)^–1 = +1.

Remember, (Y_A)² = (Y_B)² = (Y_C)² = 1.

Once again the assumption that observables — measurable physical quantities — have values whether or not they are measured, has led us down the garden path, for each time we measure the three x components, their product is invariably –1.

Caustic Sea (detail) by Eric J. Heller.