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With only one more day ahead, it is time to close some of the loose ends of the year. For me, that includes the solution of our Eastern chocolate eggs problem. It was all about applying the rules of scaling and the rules of dilation. According to the rules of scaling the volume of the larger sphere is 4x4x4=64 as large as the volume of the solid chocolate spheres. According to the rules of dilation the volume of the top half of the larger sphere is stressed to 4/3 x 32 = 42⅔, and the volume of the bottom half is compressed to ¾ x 32 = 24. This adds to 66⅔. Some participants expected the answer to be 64, since 4/3 x ¾ x 64 = 64. This misunderstanding is directly linked to the foundation of one of the benefits of diversification in investing. If you 'diversify over time’, you have to gain 33 percent (=gain by 4/3) during one period to make up for a 25 percent loss (= loose by ¾) during another period. However, if you ‘diversify over different investments’ (markets and/or strategies), a 33 percent gain on one half of your investments accompanied by 25 percent loss on the other half still brings you 4⅙ percent profit on your total investment. So, our chicken turns out to be a wise investor.
A special problem for a special event... 🐰 🥚 In this video, Harold tells you all about the chocolate spheres problem and the full text can be found below as well. Good luck 🍀 & we look forward to receiving your solution at puzzles@transtrend.com. ----------------------------------------------------- Around Easter, we eat a lot of eggs. Rumour is, the Easter Bunny delivers them. The Latin word for egg is ‘ovum’. You will recognize this in various English words that start with OV, such as oven and oval. Mathematically the oval is a very broadly defined shape. A special case of the oval is the ellipse. This is precisely defined as a collection of points that share the same sum of distances to two foci. This makes it easy to draw an ellipse using two nails, a little rope and a pencil. If we do the same with just one nail, we draw a circle. Essentially, the circle is a special case of an ellipse; the two foci coincide. But we also can literally extend a circle into an ellipse. Because the ellipse is also defined as a circle stretched in one dimension. If you compress a circle, you get an ellipse as well. And if you stretch one half of the circle and compress the other half, you don’t get an ellipse, but you still get an oval. One that looks familiar. Especially if you don’t stress and compress a circle, but a sphere. Because this is roughly what happens when an egg moves through the chicken’s oviduct. And this brings us to our problem. Suppose we have a supply of equally sized solid chocolate spheres. And we have a larger sphere which radius is four times as large as these chocolate spheres. We stress the upper half of the larger sphere by a factor 4/3. And we compress the lower half of this sphere by a factor ¾. We want to fill the resulting egg with melted chocolate. How many small chocolate spheres does this require? This problem can be solved without the use of a calculator.