(This puzzle and its solution first appeared in an article in 1945. This time the balance may be used three times to determine if there is a unique coin-and if there is, to isolate it and determine its weight relative to the others. If one is different, we don't know whether it is heavier or lighter than the others. So in two weighings, we can find a single light coin from a set of 3 Г— 3 = 9.Д«y extension, it would take only three weighings to find the odd light coin among 27 coins, and four weighings to find it from 81 coins.ДЄ more complex version has twelve coins, eleven or twelve of which are identical. It then takes only one more move to identify the light coin from within that lighter stack.

In one move we can find which of the three stacks is lighter (i.e. Now, imagine the nine coins in three stacks of three coins each. Otherwise, it is the one indicated as lighter by the balance. If the two coins weigh the same, then the lighter coin must be one of those not on the balance. To find the lighter one, we can compare any two coins, leaving the third out.

To find a solution, we first consider the maximum number of items from which one can find the lighter one in just one weighing. How can one isolate the counterfeit coin with only two weighings? The difference is perceptible only by weighing them on scale-but only the coins themselves can be weighed. Solution to the balance puzzle for 9 coins in 2 weighings, where the odd coin is lighter than the others вЂ“ if the odd coin were heavier than the others, the upper two branches in each weighing decision are swappedДЄ well-known example has up to nine items, say coins (or balls), that are identical in weight except one, which is lighter than the others-a counterfeit (an oddball). In the case n = 3, you can truly discover the identity of the different coin out of 12 coins. In general, with n weighs, you can determine the identity of a coin if you have 3 n в€’ 1 / 2 - 1 or less coins. Note that with 3 weighs and 13 coins, it is not always possible to determine the identity of the last coin (whether it is heavier or lighter than the rest), but merely that the coin is different. вЊ€ log 3 вЃЎ ( c ) вЊ‰ ДЇor example, in detecting a dissimilar coin in three weighings (n = 3), the maximum number of coins that can be analyzed is 3 3 в€’ 1 / 2 = 13. Whether target coin is lighter or heavier than others These differ from puzzles that assign weights to items, in that only the relative mass of these items is relevant. In this example, the false coin is lighter than the others.ДЄ balance puzzle or weighing puzzle is a logic puzzle about balancing items-often coins-to determine which holds a different value, by using balance scales a limited number of times. An animation of a solution to the a false coin problem involving ten coins.

Pan balance game