Ten female cadets are lined up in a column one behind the other, all facing the same direction. They are blindfolded. their drill oficer places either a red or a blue beret on each cadet's head. When the blindfolds are removed from the cadets' eyes, they can see the color of the berets of all the cadets in front of them, but cannot see the color of their own beret or of any of the berets behind them.
Starting with the cadet at the back of the line, each cadet in turn has to guess the color of her own beret. Obviously, there is no way fo the first cadet to guess the color of her beret with any confidence. However, if the cadets plan carefully beforehand, they can be sure that every other cadet will be able to guess correclty.
How can they make sure to get 5 out of 10 correctly?
If the first cadet were to declare the color of even berets could they increase the probability of correctly guessed berets?
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