# Entries for the 'Geek Challenge' Category

## 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....

## Geek Challenge Results: Baffling Birthdays

Last month, we asked you to find the odds that a class of 23 students has one or more shared birthdays. The correct answer to the Baffling Birthdays question is C: 50.7%. The winner of this month’s Geek Challenge is John Jacobsma of Dickson. His answer covered the basics, as well commented on the problem’s implicit assumptions.   There were several people who also correctly answered this month’s Geek Challenge. They are: Jesse Batche of DMC Joseph C. ...

## Geek Challenge: Baffling Birthdays

As school got back in session this fall, the first grade teachers at a large elementary school posted a list of student birthdays. The teachers noticed that of the 8 first grade classes at the school, 4 of the classes had students with duplicate birthdays. Each of the classes have just 23 students. Is their observation a statistical anomaly, or it a highly probable? What are the odds that a class of 23 students has one or more shared birthdays? A: 5.8% B: 50.0% C: 50.7% D: 75.0% A...

## Geek Challenge Results: Matrix Mind-Boggler

Congratulations to the winner of the Matrix Mind-Boggler Geek Challenge, Jordan Kuehn of the Colex Group! Jordan wrote a program which generates random matrixes using an efficient technique. He gets extra props for including a DMC logo on his program! I added extra annotations to demonstrate how the solution works. The key to solving the problem is noticing that each row and each column is used exactly once. Therefore, if each cell was the sum of numbers representing the row, and a number ...

## Geek Challenge: Matrix Mind-Boggler

Special thanks to Han Yang for providing this month’s Geek Challenge. A 4x4 matrix of numbers can be devised such that when any 4 cells are chosen where none of the chosen cells share a row or column with another chosen cell, the sum of the chosen cells is 25.  Below is an example of such a matrix with a chosen set of cells highlighted in yellow. The sum of the yellow cells is 25. Here is the same matrix, with a different set of cells, where the chosen cells also add up to 2...

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