we have 10 coins, and we aligned 9 coins as shown below. The extra coin shown is being used to turn around the aligned coins.
By turning it around like shown below, how many times would the coin turn around when it comes to its original position?
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Sign up to join this communitywe have 10 coins, and we aligned 9 coins as shown below. The extra coin shown is being used to turn around the aligned coins.
By turning it around like shown below, how many times would the coin turn around when it comes to its original position?
Since we have symmetry, let's calculate the arc touched while traversing a quarter of the distance, for example, from the 6 o'clock position to the 9 o'clock position.
We get 30 + (30 + 90 + 30) + 30 = 210 degrees.
Multiply that by four to get the total arc length of
840 degrees. Since the rotation of the coin is twice the arc traversed, we get a grand total of 1680 degrees, or 4⅔ full rotations.
Tested by rolling some poker chips around each other, they had six markings along their perimeter, which seemed to align just about exactly right.
It is
$4\frac{2}{3}$times
Calculations:
As mentioned by JS1 and ffao, I had missed the extra one rotation of the outer coin.
In terms of circular distance,
$2\pi R \implies 2$ rotations
$\frac{14}{3}\pi R \implies \frac{14}{3}*\frac{2}{2}$ rotations
$\frac{14}{3}$ rotations.
Please ignore the $\frac{22}{7}$ part :)
If a coin rotates around another coin, it completes two full rotation.
https://en.wikipedia.org/wiki/Coin_rotation_paradox
It seems it has to subtend
angles of 60 degrees at the 4 center coins and 120 degrees at the 4 corner coins, there by resulting in a total of 240 + 480 = 720 degrees, which translates to 2 complete turns