Friday, September 25, 2015

Creative Problem Solving Exercises

1. Arrange four nines to form an expression that equals 100. 

2. You are given nine coins, identical in every respect EXCEPT that one is counterfeit and slightly heavier than any of the genuine coins.  Only a sensitive balance, one with two pans and no weights, can you identify the counterfeit coin by making only two weighings?

3. Six quarters form two rows: one with three quarters, one with four.  Move one coin to make two rows, each having four quarters. 

4.  This is a real problem. There are no tricks to it.  Try your best to come up with a solution.

A man had a window in his garage door.  He decided that this window was too small as it was only one foot high and one foot wide.  To enlarge the window he used a saw to cut out the wood all around it.  By doing so he was able to double the size of the window.  But, to his surprise, when he measured it again, it was still just one foot high and one foot wide.  How can this be?

5.  A circular cake is cut into eight equal parts using only three cuts with a knife.  How can this happen?  How many different ways can this happen?

6.  There are four volumes of Shakespeare's collected works on the shelf.  The pages of each volume are exactly 2" thick.  The covers are each 1/6" thick.  The bookworm started eating on page 1 of volume 1 and ate through to the last page of volume 4.  What is the distance the bookworm covered?

Scroll down for the Answers.


1. 99 + 9/9 = 100

2. 3 & 3 1 & 1



5. Cut the cake in half, align the two halves one above the other and cut them both with a single cut, and then align the four quarters prior to the third and final cut.  Or, first quarter the cake and then make a horizontal cut halfway up the height of the cake. 

6. 5”.  As the books are lined up on the shelf, page one of volume one is 2 1/16” from the end of the stack leaving only 5” from page one of Volume One to the last page in Volume Four. 


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