Puzzle :5 men, a monkey and some coconuts

Five men crash-land their airplane on a deserted island in the South Pacific.  On their first day they gather as many coconuts as they can find into one big pile.  They decide that, since it is getting dark, they will wait until the next day to divide the coconuts.
That night each man took a turn watching for rescue searchers while the others slept.  The first watcher got bored so he decided to divide the coconuts into five equal piles.  When he did this, he found he had one remaining coconut.  He gave this coconut to a monkey, took one of the piles, and hid it for himself.  Then he jumbled up the four other piles into one big pile again.
To cut a long story short, each of the five men ended up doing exactly the same thing.  They each divided the coconuts into five equal piles and had one extra coconut left over, which they gave to the monkey.  They each took one of the five piles and hid those coconuts.  They each came back and jumbled up the remaining four piles into one big pile.
What is the smallest number of coconuts there could have been in the original pile?

Hint to puzzle : Five men, a monkey, and some coconuts

Let the original pile have n coconuts.  Let a be the number of coconuts in each of the five piles made by the first man, b the number of coconuts in each of the five piles made by the second man, and so on.

Write a Diophantine equation to represent the actions of each man.  Express n + 4 in terms of e + 1, and hence deduce the smallest possible value of n + 4.

Read More

Some Interesting Mathematical Puzzles.........

A rectangular sheet of paper is folded so that two diagonally opposite corners come together.  If the crease formed is the same length as the longer side of the sheet, what is the ratio of the longer side of the sheet to the shorter side?

Hint to puzzle : Folded sheet of paper

Draw a straight line between the two corners used to make the fold, and consider similar triangles.

------------------------------------------------------------------------------------------------------------

 Two logicians 
Two perfect logicians, S and P, are told that integers x and y have been chosen such that 1 < x < y and x +y < 100.  S is given the value x+y and P is given the value xy.  They then have the following conversation.
P:  I cannot determine the two numbers. S:  I knew that. P:  Now I can determine them. S:  So can I.
Given that the above statements are true, what are the two numbers?  (Computer assistance allowed.)
------------------------------------------------------------------------------------------------------------
 Confused bank teller 

A confused bank teller transposed the dollars and cents when he cashed a check for Ms Smith, giving her dollars instead of cents and cents instead of dollars.  After buying a newspaper for 50 cents, Ms Smith noticed that she had left exactly three times as much as the original check.  What was the amount of the check?  (Note: 1 dollar = 100 cents.)

Hint to puzzle 5: Confused bank teller

Let x be the number of dollars in the check, and y be the number of cents.  Using the fact that one dollar is equal to 100 cents, write a Diophantine equation connecting x and y.

-----------------------------------------------------------------------------------------------------------

Ant on a box 
A 12 by 25 by 36 cm cereal box is lying on the floor on one of its 25 by 36 cm faces.  An ant, located at one of the bottom corners of the box, must crawl along the outside of the box to reach the opposite bottom corner.  What is the length of the shortest such path?

Note: The ant can walk on any of the five faces of the box, except for the bottom face, which is flush in contact with the floor.  It can crawl along any of the edges.  It cannot crawl under the box.

Hint to puzzle 6: Ant on a box

The shortest path is a straight line over the top of the box.

Read More