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John M.'s Resources

Back when I was still in middle school, I was sitting at my kitchen table during a family gathering, and my uncle posed the following puzzle for me to solve: A vendor is selling apples for 10 cents apiece, oranges for 5 cents apiece, and peanuts two for a penny. Someone comes along and buys exactly 100 items for exactly one dollar. How many apples, oranges and peanuts did that person buy?   I... read more

When creating output from a Java program, you can control where line breaks occur in the text that you output by using the println method, which puts a line break at the end of whatever text is being output by the call.   However, you may need to insert line breaks into strings that you are creating, such as in the toString method of a class. How do you do it?   First,... read more

Growing up, did you ever wonder about how the devices that surround you in your home and that you rely on work? This article explores the mathematics behind the design of a simple, yet sophisticated device that might be present in your home: the electrical circuit that enables a light to be controlled from more than one switch. This circuit involves only the interconnection of simple mechanical... read more

I recently tutored a student who was working on a project to develop a dictionary program in the C++ programming language. The dictionary was kept in an alphabetically sorted array, and the student was required by the exercise to use binary search to locate entries. So, he looked up the binary search algorithm in his textbook, and found an implementation that looked similar to this: int... read more

This blog concerns how to determine the intersection between two circles in the plane algebraically. It is a problem that can crop up in a variety of situations, from gaming to tools for computer aided design to astronomy.    This problem is interesting because is it a conceptually simple problem whose algebraic formulation is nonetheless apparently complex: a system of non-linear... read more

On I.Q. tests and in other places, one is often confronted with problems of the form: “What’s the next element in the following series: 1, 4, 9, …” Technically, such questions have no right answer, because there are a multitude of ways to generate the initial elements of the series, and each way can produce a different result for how the series should continue. What is being sought is... read more