Ok, there two yellow dots on person X and person Y. Person Z has a blue dot. They open their eyes.
X raises him hand because he sees Y’s yellow dot. He also sees Z’s blue dot.
Y raises him hand because he sees X’s yellow dot. He also sees Z’s blue dot.
Z raises him hand becasue he sees both X and Y have yellow dots.
Now both X and Y know they have to have yellow dots because they can see one blue dot and three are required for all three to raise their hands (see below). Z doesn’t know what colo his dot is.
If there were no yellow dots nobody will raise their hand.
IF there one yellow dot only two will raise their hands. Let’s say X has the yellow dot.
X will see two blue dots won’t raise hand.
Y will see one yellow and one blue and will raise his hand.
Z will see one yellow and one blue and will raise his hand.
So if all three raise their hands there has to be at least two yellow dots. And if there is only two yellow dots two people will know they have a yellow dot. If there is confusion it requires three yellow dots if the players are smart.