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

Example 1. What is eleven cut in half? Solution 1 Solution 2

Example 2. Will nine apples fit in four baskets with an odd number in each? Solution

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

More Challenge Sought?

Example 3. Can a circular pizza pie be divided into exactly eight equal area pieces with just three straight line cuts? Solution.

Example 4. What would a half plus a third be? Are you sure? If interested in this issue, click Fractions.

Example 5. For a more complex question that relates to the numeric ideas behind computing please click here Sequence.

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 Parity, Hierarchy, Exponents, Algebra in the table above are used in highly technical senses in Engineering, Computing, Science, and Mathematics. Even if they are unclear now, the puzzles are entry points to the notions. They are so useful that people found it necessary to create condensed writing systems to describe these ideas.

The following example leads to another key notion.

Example 6. If a herring and a half costs a penny and a half, how much do two herrings (or six herrings) cost? For a solution please click Ratio.

Example 7. Complex weighing puzzle: it involves a an unusual twist ... to what is familiar (as a class of puzzles) :

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.

Example 8. Another weighing puzzle with knowledge of good and bad coin weights.

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.

Example 9. A man enters a restaurant. He orders, eats, and seeks to pay for his dinner. He finds only the owner available. The owner tells him "That's o.k. Just open the cash-box, put in the amount that is there, and take out one thousand." The same thing occurs exactly as stated in the preceding three sentences to two other men. After the third one is done there is five thousand in the cash-box. How much was there originally (before the first man entered the restaurant)? To see a solution please click here Cash.

Example 10.A certain scale (again, not a beam balance) can be used only once. There are ten sets of gold coins, one in the first, two in the second, and so forth until the tenth which has ten coins. In each set is all the coins are either good or fake, and there is one set that is composed of fakes. All good coins weigh the same. All the fakes are also the same weight. Fakes are either heavier or lighter than good coins by a certain known amount, but which is true isn't known in advance. Find a way to determine how many coins are fakes, and whether they are heavy or light, compared to a good coin. To see a solution please click here Weigh Once.

Example 11.( What should the eleventh puzzle be?) To make a suggestion click here. One idea was a UCLA professor's classroom visit: to see an email excerpt describing an elementary school puzzling weight activity please click Bag It.

© Allen Klinger May 31, 1998