Brain Teasers
16 Coins
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?
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?
Hint
Stars and pentagonsAnswer
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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Comments
Too tough! I loved it, but I didn't get it even with the clue. And I hate using the clues in the first place!
Great teaser!
Great teaser!
I did look at the hint to get myself started. I had a different possibility figured out, compared to your answer. It works on the same principal as your solution, but you will get 16 rows for 16 coins... with 4 coins in each row. I do suppose your answer is the correct one, though Dynamic teaser and reasonably tough.
LOL
I had almost this same problem on during a matth computition
I had almost this same problem on during a matth computition
damn, that was a tough one...! I had pentgrammas, pentagons arround the star, david stars and so on... put a star within a star... didn't think about that! Great!
Brilliant!
Pizzazz2u:
Could you explain how you can get the 16 rows???
Could you explain how you can get the 16 rows???
WOW!! you got me!!! one point for you
It was clever, but the hint gave it away.
Jan 19, 2009
It would be better if the problem read as "15 lines of 4 coins" instead of "15 rows of 4 coins". Would make it less ambiguous.
Wow, I don't think I would have gotten this in a million years Very creative mind you got!
wow, that was hard! Would not have got it without the hint. Came to me after that, tho. Good one!
Definitely needed the hint. Good teaser.
Fantastic and difficult tease. I definitely needed the hint.
My solution was very similar, but a bit different.
Draw the star with its internal pentagon. Then draw the lines from the each point of the star to the opposite vertex of the internal pentagon. Put coins at every intersection of lines. It is the given solution without the internal star.
However, each line in the original star has five coins on it, which can make two line segments of four coins. So I agree, my drawing only has ten lines, but 15 rows of four different coins. The given solution avoids this semantic distinction.
My solution was very similar, but a bit different.
Draw the star with its internal pentagon. Then draw the lines from the each point of the star to the opposite vertex of the internal pentagon. Put coins at every intersection of lines. It is the given solution without the internal star.
However, each line in the original star has five coins on it, which can make two line segments of four coins. So I agree, my drawing only has ten lines, but 15 rows of four different coins. The given solution avoids this semantic distinction.
Glad you liked it and I see how you came up with your answer too, but also see that slight issue that mine avoids. Thanks again.
Would have been great to specify that a straight line (15 overlapping segments of columns of size 4) is not a valid answer
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