Martin Gardner
Image source: Martin Gardner

Martin Gardner
Image source: Martin Gardner

Martin Gardner's puzzles

Martin Gardner (October 21, 1914 – May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing micromagic, scientific skepticism, philosophy, religion, and literature—especially the writings of Lewis Carroll and G.K. Chesterton.
Gardner was best known for creating and sustaining general interest in recreational mathematics for a large part of the 20th century, principally through his Scientific American "Mathematical Games" columns from 1956 to 1981 and subsequent books collecting them. He was an uncompromising critic of fringe science and was a founding member of CSICOP, an organization devoted to debunking pseudoscience, and wrote a monthly column ("Notes of a Fringe Watcher") from 1983 to 2002 in Skeptical Inquirer, that organization's monthly magazine. He also wrote a "Puzzle Tale" column for Asimov's Science Fiction magazine from 1977 to 1986 and altogether published more than 100 books.(Wikipedia)


Toothpick Giraffe Puzzle.


Toothpick Giraffe Puzzle

Five toothpicks form the giraffe shown above. Change the position of just one pick and leave the giraffe in exactly the same form as before. The re-formed animal may alter its orientation or be mirror reversed but must have its pattern unchanged.


     

Toothpick Giraffe Puzzle
Turn it clockwise, you get the mirrow image of the original with unchanged pattern.
Toothpick Giraffe Puzzle


The Counterfeit coins.


Counterfeit coins

You have 10 stacks of coins, each consisting of 10 coins. One entire stack is counterfeit, but you do not know whick one. You do know the weight of a genuine coin and you are also told that each counterfeit coin weighs 1 gram more than it should. You may weigh the coins on a pointer scale. What is the smallest number of weighings necessary to determine whick stack is counterfeit ?


  

Answer: If you know the weight of a genuine coin (suppose it is exactly 10 grams), You need to take the reading from the scale only once in order to find the stack containing the counterfeit coins.
First, identify the stacks by numbering them from one to ten. Then place on the scale one coin from stack#1, two from stack#2, 3 from stack#3, etc. up to all ten from stack#10.
Had there been no counterfeit coins, the scale would read (1+2+3+4+5+6+7+8+9+10)x10 = 55 x 10 = 550 grams.
If the counterfeit coins are in stack#1, the weight will be 551 grams, since only one coin from stack#1 is included and the counterfeit coin weighs 1 gram more than the genuine coin.
If the counterfeit coins are in stack#2, the weight will be 552, since two coins from stack#2 are included.
In general, the weight should be 550 + N grams and N will be the number of the stack containing the counterfeit coins!


 

Balance scale puzzle (A counterfeit one in 9 coins).


9 coins

A well-known example has nine items, say coins, that are identical in weight save for one, which in this example we will say is lighter than the others—a counterfeit. The difference is only perceptible by using a balance, but only the coins themselves can be weighed, and the balance can only be used twice.

Is it possible to isolate the counterfeit coin with only two weighings?


     


Balance scale puzzle (A different one in 12 coins).


12 coins

A more complex version exists where there are twelve coins, eleven of which are identical and one of which is different, but it is not known whether it is heavier or lighter than the others. This time the balance may be used three times to isolate the unique coin and determine its weight relative to the others.