Entertain, amuse ... and take time to solve.

More examples and many images (long time to download) are available. To view them please click Some Thoughts.

More Challenge Sought?

Each example is more than a way to test your ability to reason in an unfamiliar situation. They are short introductions to mathematical tools.

Example 1. Number Representation, Use of Symbols |
Example 2. Odd and Even, Parity, Hierarchy |

Example 3. Multiplication and Exponents |
Example 4. Arithmetic, Algebra |

The words

The following example leads to another key notion.

The king suspects that one of five gold bars may be counterfeit. All genuine gold bars have the same weight (which is unknown, for some reason) but a counterfeit bar would weigh more or less than a genuine bar. The king has a scale (not a beam balance like we usually have in such puzzles, but a scale which gives the precise weight of whatever you put in its pan) and wants to find out if one of the bars is counterfeit, how much a genuine bar weighs, and, if one of the bars is counterfeit, what its weight is. This would be trivial in five weighings, but the king is in a hurry and wants it done in three. Is this possible, and if so how? Note that you are allowed to weigh up to five bars simultaneously if you wish. To see a solution please click here Three Weighings.

You have again a scale, not a balance, and four coins. Any of the coins could be defective. Each bad coin has the same known weight. Likewise any of the coins could be good. Again, each good coin has the same known weight. FInd a method to find all the coins that are good and every bad coin in exactly three weighings. To see a solution please click here Coins.

© Allen Klinger May 31, 1998