Oh no! You are trapped in a lost underground cavern, dimly lit by torches. Before the locked egress stands a stone bench with nine gold coins, a two-pan balance, and a carved statue with a coin-sized slot--sort of like a giant scary piggy bank. You recognize some runes carved into the surrounding architecture. Fortunately, you studied runes last year so you can read them. They say: “The masses of eight equate; only the one with greater weight shall unlock the gate. To identify the heavy coin, you may use the scale but twice. Attempt any more weighings than two, and you shall never pass through.” How will you find the heavier coin using only two weighings on the two-pan balance scale? If you can do it, you can drop the heavy coin into the slot and you’ll be free. (And as you leave, will you dare to take the other eight coins with you?)
Solution
Name the coins
First weighing: Weigh two groups against If the first group is heavier than the second, then the heavier coin is or If the second group is heavier, then the heavier coin is or If the scale balances, the heavier coin is one of or
Second weighing. Put one of the three coins isolated by the first weighing in each pan, setting one to the side. Make the easy deduction!