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More ways to get Braingle...

16 Coins

Logic puzzles require you to think. You will have to be logical in your reasoning.

 

Puzzle ID:#33211
Fun:*** (2.8)
Difficulty:*** (3.04)
Category:Logic
Submitted By:fishmedAus******mod

 

 

 



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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Comments

scallioAus*
Sep 28, 2006

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!
Pizzazz2uAus*
Sep 28, 2006

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.
tmkingus
Oct 07, 2006

LOL

I had almost this same problem on during a matth computition
PhalanxAlu*
Oct 09, 2006

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!
qwertyopiusa*
Nov 29, 2006

Brilliant!
qwertyopiusa*
Nov 29, 2006

Pizzazz2u:
Could you explain how you can get the 16 rows???
jrg1612*us
Dec 07, 2006

WOW!! you got me!!! one point for you
t4mtAcn*
Jan 03, 2007

It was clever, but the hint gave it away.
(user deleted)
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.
opqpop
Jan 30, 2010

Wow, I don't think I would have gotten this in a million years Very creative mind you got!
papiermeisterAca*
Dec 03, 2010

wow, that was hard! Would not have got it without the hint. Came to me after that, tho. Good one!
bradon182001*us*
Dec 03, 2010

Definitely needed the hint. Good teaser.



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