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What is the total number of sides on the loonies in the smallest non-trivial 6-pointed star?
A loonie is the Canadian 1 dollar coin which is not quite round, it is a hendecagon. There have been recent questions here about polygonal and stellar numbers, numbers of coins which can be arranged into filled-in polygons or stellated polygons (stars). Usually such arrangements begin with a single coin, the trivial case. I want a recognizable star, or what some might recognize as a snowflake pattern, so more that one coin is required. Count the total number of sides on the loonie coins required to make the smallest recognizable (and filled-in) six-pointed star.
Happy Canada Day!
@Julius: A six-sided coin would fit together more nicely, but the only 6 sided coin I'm aware of comes from Myanmar (where snowflakes are less common) and that coin hasn't been minted in over 20 years. Furthermore, with a 6 sided coin, there would be a grand total of only 78 sides. That is too few for Canada Day, but Myanmar has more that 20 years yet to reach that anniversary.
2 Answers
- gianlinoLv 71 decade agoFavorite Answer
Well, that is a tricky one.
Let's call A the number of coins,
A is solution of the equation
A = 1 + 4 + 3 + 4 + 1.
To see this just count the coins line by line. There are 5 lines each of which has 1, 4, 3, 4, and 1 coins, hence the equation. From that you can safely bet that A is either equal to 13 or at least quite close.
We then come to the number of sides of each coin. That too is hard but there is a hint: "hendecagon" Thank god wiki saves us once more 11 is the number we are looking for.
So the final blow is this: what is 11 * 13 ???
Well it's (12 + 1) (12 - 1) = 12^2 - 1^2 = 144 - 1 = 143
ANSWER 143
Source(s): http://en.wikipedia.org/wiki/Hendecagon
