# math

• March 4, 2021

Motor-Cycling

This brainteaser looks so simple, but it’s not! There are 50 bikes with a tank that has the capacity to go 100 km. Using these 50 bikes, what is the maximum distance that you can go?
• January 22, 2021

Parking Problems!

This week, I’m going back to the good ole engineering brainteaser. This one is for all you who have to fight to find a parking spot at work! The probability of finding the parking slot occupied is 1/3. You find it empty for 9 consecutive days. Find the probability that it will be empty on the 10th day. You can find this brainteaser and many others at GineersNow.com: Can You Answer These Brain Teasers Like a Silicon Valley Engineer?
• February 17, 2020

The “Holey” Sphere

[From the website of Dr. Donald Simanek—see further down.] Browsing Martin Gardner’s books I stumbled on this diabolical puzzle. Gardner calls it “an incredible problem”. He traces it back too Samuel I. Jones’ Mathematical Nuts, 1932, p. 86. It is seen on the web in various forms, often ambiguous in wording, along with endless discussions often leading nowhere. I have tried to restate it to remove ambiguity (which isn’t easy). A hole is drilled completely through a sphere, directly through, and centered on, the sphere’s center. The hole in the sphere is a cylinder of length 6 inches. What is the volume of the remainder of the sphere (not including the material drilled out). You’d think there’s not enough information given. But there is. The solution does not require calculus. Gardner gives an insightful solution that requires only two sentences, including just one equation. Visit From mathworld.wolfram.com for more info. The answer is provided by Doctor Donald Simanek, Professor of Physics Emeritus at Lockhaven University. Visit Donald Simanek’s page at Lockhaven.edu for more brain-bending physics puzzles! Now that’s an interesting answer! Keep scrolling down… Wanna see a video answer to the brainteaser? This video was created by Tom McNaney Jr., Generalist Applications Engineer, Fellow at PTC (the company that I currently work for). Here is his detailed approach to the brainteaser using PTC’s flagship CAD program Creo Parametric! For the Holey Sphere challenge, Creo Parametric says the volume is 113.097 in^3. Interestingly, the volume remains constant regardless of the sphere Radius. Cool. I have no idea what the mathematical formula is, but probably 4/3*Pi*(something)^3. Who needs advanced math when they have Creo or Mathcad?