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The answer is pretty simple.

1. The strategy is that they should agree to write down the same colour(either red or black), irrespective of what they see on the opposite persons forehead

2. Same as above. This time all of them should agree to write any single suit.

By probability, at least one of them will get it right.

[Edit]: Didn't put it correctly before

1 They should write their own color, so this is not a winning strategy. [Spoiler] As stated by other the winning strategy is that one says always the other person's color and the other say the opposite. That's because or the color are the same or are different.

You're right

This won't work, it's perfectly possible that they draw the same color; which could be the opposite of what they agreed to write down.

True. The logic is flawed

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