|Fun:|| (2.8) |
|Difficulty:|| (3.04) |
Johnny was given 16 coins by his older, somewhat meaner brother, Mark. He told him that he could keep them all if he could place all 16 on the table in such a way that they formed 15 rows with 4 coins in each row.
After 10 minutes, Johnny walked away with the coins and Mark, after complaining futilely to his mother, left with nothing.
How did Johnny place the coins?
Answer:If you draw a 5-pointed star with all sides of equal length, you will create a pentagon in the middle with all 5 sides of equal length. Then draw another 5 pointed star, upside-down, using the 5 points of the interior pentagon as the points of the inner star, This will give you another 5-sided pentagon in the interior of the second, smaller star.
Now, take your 16 coins and place 5 on the outside points of the outside star. Then place 5 more on the points of each of the two pentagons you have created. Finally, place the last coin in the dead center of this drawing.
The lines are as follows:
5 lines for the actual drawing of the outside star
5 lines for the actual drawing of the inside star
5 lines that start from any outside point of the outside star and go to the opposite point of the inside star, passing through 1 point of the inner pentagon, the dead center coin on the way.
Total lines: 15
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