Hat puzzle 5 prisoners answer correctly and 5 do not. Note that the prisoners cannot find a strategy guaranteeing the release of more than 5 prisoners. Indeed, for a single prisoner, there are as many distributions of hat colors where he says the correct answer than there are where he does not. Hence, there are as many distributions of hat colors where 6 or more prisoners say the correct answer than there are where 4 or fewer do so. In this variant, a countably infinite number of prisoners, each with an unknown and randomly assigned red or blue hat line up single
Cowboy hat "The term ten-gallon did not originally refer to the holding capacity of the hat, but to the width of a Mexican sombrero hatband, and is more closely related to this unit of measurement by the Spanish than to the water-holding capacity of a Stetson." The Stetson hat company boasted that the tight weave of most Stetsons hats made them sufficiently waterproof to be used as a bucket. Early print advertising by Stetson showed a cowboy giving his horse a drink of water from a hat. However, even the Stetson company notes that a "ten-gallon" hat holds only 3 quarts (about