Overview Challenge #1 Challenge #2 Bonus Challenge

The following logic problems and challenges are an opportunity for you to show us your independent thinking, creativity, and initiative in applying for a position at BTG.

Please email answers to jobs@boylstontech.com. Please be sure to include contact information and a recent resume with your submission.

If you are a non-U.S. candidate, please click here for our International Candidate Challenge.

A room contains a row of 100 light bulbs. Below each light bulb is a switch to control the bulb above. To begin, each bulb is off. As a bright idea Solution Engineer, you decide to pass through the row, flipping each light on, one-by-one. Your next bright idea is to make a second pass, this time flipping the switch for every 2nd light (#2, #4, #6…..#100), turning half of the lights off. You make a third pass toggling the switch for every 3rd light, then another pass toggling every 4th, then 5th, then 6th, all the way up to your 100th pass when you change the setting of only the 100th light. First, without actually simulating the problem, tell us which lights will be in the ON position once you’ve run the simulation, and why.

Next, code a simulation of this challenge in PHP. Your simulation should accept an iteration number (1-100) and output the state of all light bulbs for that iteration.

Email your submission to jobs@boylstontech.com.

At the annual Egghead Convention, 126 eggheads gathered from around the world to hear Professor Eggstein's latest findings in the world of Eggonomics. Suddenly, and without warning, a rogue Eggsterminator entered the convention hall, armed with what else but raw eggs, ready to take out every egghead in the room. Pleading for their dignity, the eggheads scrambled to negotiate with their attacker. After much talk, the attacker agreed to give the eggheads a chance to minimize casualties. The attacker would require the eggheads to line up single-file, all facing forward. Some eggheads would be required to wear yellow hats, while others would wear white hats. The eggheads would be able to see everyone in front of them, along with their hats. However, no egghead would be able to see his own hat or those of the eggheads behind him. The attacker would then go to each egghead one-by-one and ask the color of his hat. If the egghead answered correctly, the Eggsterminator would spare the egghead from being hit with one of his eggs. If the egghead was incorrect, he'd be hit point blank. As one last concession, the attacker will allow the eggheads to meet beforehand and talk amongst themselves about their situation. As one of the eggheads, what strategy would you propose to limit the number of casualties? How low can you get the number of possible casualties?

Code a solution to simulate your strategy in action in either PHP. Code will be assessed for elegance and efficiency, while conforming to the real-world constraints of the problem.

Email your submission to jobs@boylstontech.com.

This one’s pretty straightforward. Look at the diagram below. First, fill in the question marks with the appropriate die face and missing numbers.

Next, code a simulation of this problem in PHP. Your solution should accept user input for the size constraints of a two-dimensional array, and output a randomly generated field of dice faces, along with tabulating the value of each row, column, and diagonal.

Email your submission to jobs@boylstontech.com.