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 – if the odd coin were heavier than the others, the upper two branches in each weighing decision are swappedĪ 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 − 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. ⌈ log 3 ( c ) ⌉ įor example, in detecting a dissimilar coin in three weighings (n = 3), the maximum number of coins that can be analyzed is 3 3 − 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.Ī 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. Continued abuse of our services will cause your IP address to be blocked indefinitely.An animation of a solution to the a false coin problem involving ten coins. Please fill out the CAPTCHA below and then click the button to indicate that you agree to these terms. If you wish to be unblocked, you must agree that you will take immediate steps to rectify this issue. If you do not understand what is causing this behavior, please contact us here. If you promise to stop (by clicking the Agree button below), we'll unblock your connection for now, but we will immediately re-block it if we detect additional bad behavior.
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