### Brain Teasers

# Coin Circle

Place any circular coin down flat on a table. Can you do a simple calculation to estimate to the nearest whole number of coins the maximum number of coins of the same size that will fit in a concentric circle around the center coin? Each surrounding coin must touch the center coin and also lie flat on the table

### Hint

Use the formula Circumference = pi x diameter.### Answer

SixSince the surrounding coins will touch approximately at their diameters (d) we are looking for how many diameters of this size coin there are at the circumference (C) where the coins touch. This circumference falls at approximately 2 x the radius (r) of the coins from the center of the circle. The diameter of this circumference would be approximately 4 x r or 2 d. The circumference would then be pi (3.14) x 2 d = 6.28 d. Since each diameter of a coin represents one coin there would be approximately 6.28 coins. The coins would only touch at their widest part or diameter if they were laid out in a straight line. Since they are in a circular pattern they actually touch slightly below their widest diameters so the actual diameter of the circumference is slightly less than 2d. Thus we know that there would be slightly fewer than 6.28 coins and the closest whole number estimate is six.

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