Logical Puzzles Hard 5 min

You have 12 coins. One coin is counterfeit and may be either heavier or lighter than the others. Using a balance scale, what is the minimum number of weighings needed to identify the counterfeit coin and determine whether it is heavier or lighter?

Hint

Each weighing has three possible outcomes.

Answer

3 weighings.

Explanation

There are 24 possible states because any of the 12 coins can be either heavier or lighter. Three balance-scale weighings provide up to 27 different outcome sequences. A standard three-weighing strategy can identify the counterfeit coin and determine whether it is heavier or lighter.

Step-by-Step Solution

There are 12 × 2 = 24 possible counterfeit states.
A balance scale has 3 possible outcomes per weighing.
Two weighings provide 3² = 9 outcome patterns, which is insufficient.
Three weighings provide 3³ = 27 outcome patterns, allowing the standard 12-coin solution.

6 puzzles

Six people A, B, C, D, E and F sit in a row. A sits immediately to the left of B. C sits immediately to the right of D. E sits at the extreme left. F sits at the extreme right. Who occupies the two middle positions?

18 views Logical Puzzles

Medium

Five students P, Q, R, S and T scored different marks. P scored more than Q but less than R. S scored less than Q. T scored more than R. Who scored the highest and who scored the lowest?

15 views Logical Puzzles

Hard

Four tasks W, X, Y and Z must be completed one at a time. W must be before X. Y must be before Z. X must be before Y. Which task must be completed third?

26 views Logical Puzzles

Hard

Seven runners finish a race. A finishes before B. B finishes before C. D finishes after C. E finishes before A. F finishes after D. G finishes before E. Who must finish before everyone else?

17 views Logical Puzzles