In a group of ten coins there are either one or two fake coins and the rest are real. The fakes can be distinguished from the real coins only by weight. If there are two fake coins they will be equal weights.
Find a strategy to identify the fake coin or coins which uses only a balance scale no more than five times.
i am saying that the fake coins are heavier. if they are lighter do it the opposite way. place five coins on each side. if one side is is heavier that contain atleast one fake coin. measure two on each side from that group. the heavier one contain the fake coin. measure those two to find the fake coin match it up with the coin set aside to see if that is fake or not. if the two sets of two are equal it is because the coin set aside is fake or two fake coins are balancein each other out. compare one of the sets of two against each other. the coin heavier is the fake one. do the same with the other group. if they are equal than the coin aside is fake. if the two groups of five are equal there are two coins beacause there are only one or two. then measure two coins on each side from one of the groups. if one is heavier that cointain the fake coin. measure thoses two coins against each other to see what one is fake. if they are equal the fake coin is the one placed aside. do the same with the other side and you have both fake coins.