Suppose that we are allowed to drill a cylindrical hole of any radius through the center of a unit ball or a unit cube in a given direction. Which radius will maximize the total exposed surface area (ESA) of the finished object? If we are allowed to drill two or three mutually orthogonal cylindrical holes of the same radius, which common radius will maximize the total ESA?

We propose a new puzzle: Label the eight vertices of a cube using distinct integers between 0 and 12 (both inclusive) such that the induced labeling of each edge, given by the sum of the labels of its end points, causes the 12 edges to be labeled with distinct odd numbers 1, 3, . . . 23.Any solution to the puzzle is called a super odd-sum labeling. We deftly discover all the super odd-sum labeling of the cube.

What is the shape of the novel coronavirus which has turned our world upside down? Even though under a microscope it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still obeying the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure.

Our musings are split into four parts. We fondly hope that while readers await the future parts to appear, they will indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.

What is the shape of the novel coronavirus which has turned our world upside down? Even though it looks dull, unattractive, and even disgusting under a microscope, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure.

Our musings are split into four parts. We fondly hope while readers wait for the future parts to appear, they will indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.

What is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a microscope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathematician contribute to this effort? We take a purist’s point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from reality but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind’s creation, beckoning others to join in the pleasure.Our musings are split into four parts. We fondly hope whilereaders wait for the future parts to appear, they will indulgein their own musings, tell others about them, and propagatethe good virus of mathematical thinking.

What is the shape of the novel coronavirus (n-CoV) which has turned our world upside down? Even though under a micro­scope, it looks dull, unattractive, and even disgusting, creative artists have attributed to it bright colors, made it look pretty, and depicted it as a thing of beauty. What can a mathemati­cian contribute to this effort? We take a purist's point of view by imposing on it a quasi-symmetry and then deriving some consequences. In an idealistic world, far removed from real­ity but still constrained by the rules of mathematics, anyone can enjoy this ethereal beauty of the mind's creation, beckon­ing others to join in the pleasure. Our musings end with this Part 4. We fondly hope readers have benefited from our suggestion that they indulge in their own musings, tell others about them, and propagate the good virus of mathematical thinking.

We set out to find the shortest closed curve that connectsthree objects – each of which is a point, a line or a circle –on a plane. The solution is sometimes trivial, sometimes easy,sometimes hard and sometimes impossible. We hope readerswill be inspired to provide alternative justifications/answers.

Suppose your father gives you a hollow cylindrical knife asa birthday gift, and your mother buys you a bag of potatoes.When the knife is pressed into a potato and the outer excess isremoved, the interior of the knife yields a cylindrical core. Bypressing the knife into a potato from several strategically chosendirections, you can construct some solids of intersectionsuch that all faces are identical or one of two distinct shapes.

A bottle contains 7 Type A and 7 Type B candies. Each morn­ing, you select two candies at random: If they are of opposite types, eat them both; otherwise, eat one and return the other to the bottle. Continue until all candies are eaten. If ever the bottle contains only one candy, select and eat it. How many distinct candy sequences are possible?

If you pick three points independently and uniformly in a disc or a ball, what is the probability that the random triangle with vertices at these points will be acute?