# Entries for the 'Geek Challenge' Category

## DMC Quote Board - September 2018

Visitors to DMC may notice our ever-changing "Quote Board," documenting the best engineering jokes and employee one-liners of the moment.

## Geek Challenge: A Place in the Sun

You are an engineer on site in Lebanon, Kansas. At sunrise on the vernal equinox, you hop in your hovercar and start driving directly toward the rising sun along the ground at a constant 60 mph. You continue driving in this way until the sun sets. What are your coordinates when you stop driving? Parameters •    Coordinates of Lebanon, Kansas: 39°48′38″N 98°33′22″W •    Vernal Equinox: September 22, 2018 • ...

## Geek Challenge Results: Primetime Telephone Numbers

In last month's Geek Challenge, we asked what number contains 22 primes?  This was a unique problem that needed to utilize at least a little bit of computation (to check if something is prime or not). Luckily, prime calculators are a dime a dozen across the interwebs and many computer languages have a “prime check” method built in. Congrats to our winner, Alex Bruno! A few people commented on the problem being too constrained, giving the amount of included prime n...

## Geek Challenge: Primetime Telephone Numbers

I was listening to the radio, and some self-proclaimed geek said that her phone number was "seven prime numbers." At first, I interpreted this as "seven prime digits," which is probably what she meant. But then it got me thinking, 23 has three prime numbers in it (2, 3, and 23), and 373 contains six primes! The most primes you can pack into a seven-digit number is 22, so what number contains 22 primes?  Remember: neither 0 nor 1 are prime; and 5003 contains 5...

## Geek Challenge Results: The Perfect Bracket

Congratulations to Grant Anderson of DMC, Michael Deck of Avant, and John Jacobsma! All correctly answered last month’s Geek Challenge with C: 93.424%! Michael Deck is this challenge’s winner for his extensive solution that not only solves the proposed problem but handles more involved aspects not considered by the OP.  Michael’s solution is below. 1 Introduction The problem is stated here. 2 Solution 2.1 Main solution First, we set forth the probability ...

## Geek Challenge: The Perfect Bracket

With March Madness wrapping up and everyone’s brackets broken once again, this month’s Geek Challenge is about what it might take to build the perfect bracket. It's time for all the mathletes out there to show off their skills. Imagine that for every game in the NCAA tournament you know the probability p for the favored team to win the game. For simplicity’s sake, let’s assume p is the same for all the games in the tournament. You fill out your bracket to reflec...

## Geek Challenge Results: Eccentric Traveler

The results are in! February's Geek Challenge winner is Grant Anderson of DMC. Grant's clever breakdown of the problem is shown below. Grant's Solution There are five classifications of locations that satisfy this riddle (at least on the surface): As mentioned in the riddle itself, the North Pole. All locations one-mile north of the one-mile long parallel of latitude in the Northern Hemisphere. All locations one-mile north of the one-mile long parallel of latitude in the Southern He...

## Geek Challenge: Eccentric Traveler

This month's geek challenge focuses on some strange sightseeing aspirations of an eccentric traveler. Our eccentric traveler's odd expedition begins by considering the following riddle: You walk one mile South, then one mile East, then one mile North. When you finish walking you are at your original location. Where are you? After initially deducing the solution to be the North Pole, our eccentric traveler realized there were other starting locations in ...

## Geek Challenge Results: Infinipool

The results are in! Two people correctly answered December's geek challenge. Ken Brey of DMC and Jesse Batsche of DMC both identified the correct percentage as D: 60-65%. Ken supplied an exact solution for the probability as the grid of pool balls becomes infinitely large. However, Jesse is this month's winner because he wrote a really cool LabVIEW program to solve the problem! Ken's Exact Solution Where X and Y represent the row and col...

## Geek Challenge: Infinipool

December’s Geek Challenge is about trying to make pool shots on an infinitely large pool table.  To describe the challenge, let’s look at a 3x5 grid of pool balls with the cue ball positioned in the center. We want to know what the odds are that we can hit a ball chosen at random with the cue ball (without jumping or curving around other balls). Looking at the possible cue ball paths, we see we can hit any ball except the 6 or the 9 because the 7 and 8 balls get in the way...

## Geek Challenge Results: Crossing of the Chords

Thirteen people correctly answered the Crossing of the Chords Geek Challenge by selecting C: 70 intersections. In their explanations, two very distinct methods were demonstrated to arrive at the general equation for intersections as a function of perimeter points. This month’s winners are John Jacobsma of Dickson, Devon Fritz of DMC, Sudeep Gowrishankar of DMC, and Adnaan Velji of DMC. They used a Combinations method to arrive at the method very efficiently.   To give proper contex...

## Crossing of the Chords

A number of points (N) are distributed along the circumference of a circle. Every point is connected to every other point by a chord. The points are spaced unevenly such that no more than two chords intersect at a common point inside the circle.     As demonstrated in these figures, when there are 4, 5 and 6 perimeter points, there are 1, 5 and 15 internal chord intersections respectively. If N=8 (circle with 8 points on the perimeter), how many internal cord intersections are...

## Geek Challenge Results: Define the Doodling Curve

Last month’s Geek Challenge was to find the limiting curve created by drawing lines on graph paper in a certain pattern.   The correct answer is C, and the values for the constants were 1, 2, and 1. These three people answered the question correctly: Andrea Gotti of Milan Polytechnic, Adnaan Velji of DMC, and Dan Freve of DMC. Of these, the winner is Andrea Gotti. Andrea solved the problem as follows: Each line of the paper doodle passes through two points. Those points will ...

## Geek Challenge: Define the Doodling Curve

A graph-paper doodle connects each point on the x-axis with a consecutive point on the y-axis with a straight line. Within a defined boundary, the positions on the x-axis move away from the origin as the positions on the y-axis move toward the origin. The resulting shape fills a defined curving boundary with a pretty pattern. The geek challenge for this month is to define the curve generated by these straight lines. Focusing on the lines in the positive x and y quadrant, select the functi...

## Geek Challenge Results: What's Your Angle Equilibrium?

Three people successfully solved the Equilibrium Angle Geek Challenge. They were Dan Freve of DMC, Brandon Williams of Yaskawa and Jeff Winegar of DMC. The correct answer is C: a ≈ 50 degrees The interpretation of this answer is that if the bar is released from the wall at an angle <50°, it will fall back to the wall with the bar still suspended from its bottom point. If the angle is >50°, the angle will increase, the bar will invert and ultimately dangle from its t...

## Geek Challenge: "What's your angle Equilibrium?"

A uniform bar has identical frictionless wheels on each end. The distance between the axle centers is 1m. The bar is suspended by a rope attached to the lower axle and to a fixed point offset from the wall a distance that equals the wheel radius. The length from the attachment point to the axle center is 1.5m. Neglecting the weight of the rope, at what angle (a) will the system rest at equilibrium? A:  a ≈ 30 degrees B:  a ≈ 45 degrees C:  a ≈ 50...

## Geek Challenge Results: A Balancing Act

Several entrants correctly answered the Balancing Act Geek Challenge. The correct answer is B, the scale tips to the right.   Correct answers were received from Tim Jager of DMC, Devon Fritz of DMC, Brandon Williams of Yaskawa, Ian Schleifer, and Gareth Meirion-Griffith of DMC. Many people answered that the scales would tip to the left. The intuitive answer points that way. Since the pool ball is suspended externally, it is easy to attribute all of its weight to the external supp...

## Geek Challenge: A Balancing Act

An apparatus is constructed as shown below comprising equivalent buckets of water.  The buckets and water were placed on the scale first, and it balanced.  Then two suspended balls of equal diameter are added in the configuration shown.  One is wooden, and floats.  It is suspended from the bottom of the bucket.  The other is a pool ball that sinks.  It is suspended externally. Assuming the weight and displacement of the strings is not significant, what happens ...

## Geek Challenge Results: Infinite Snowman Stumper

December’s Infinite Snowman Geek Challenge winner is John Jacobsma of Dickson.  Adnaan Velji of DMC also answered all questions correctly.  The determination of best answer goes to John due to his elegant solution for the Center of Mass.   The correct answer to the primary questions is B, that the snowman will be 3m tall.  The extra credit answers are that its construction will not consume more than the available snow, and that the belly button at the center of mass ...

## Geek Challenge: Infinite Snowman Stumper

Ever wanted to construct the most mathematically magnificent snowman of all time? Here’s your chance. Figure out the Geek Challenge below…and don’t forget to actually build your snowman! A snowman is to be built with an unlimited number of spherical snowballs where the diameter of each ball is 2/3 the diameter of the ball below.  If the first ball is 1m diameter, how tall will the completed snowman be? A:  2m B:  3m C:  5m E:  Infinitely tall....

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