Category: Mathematics
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Consider this problem: An absent-minded American mathematician has difficulty remembering his seven-digit phone number until he notices that, when he reverses the digits, he gets another seven-digit phone number that is a factor of his own phone number. After this point, he never has trouble with his number again. What is his phone number? (This…
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The Puzzle [mathjax]Here’s an interesting puzzle: The hostess of a baby shower devises a game in which sixteen tokens are placed in an opaque bag. The tokens are all either pink or blue, and they’re otherwise identical in shape, weight, texture, and so on. Two guests are chosen. The first guest chooses a single token…
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Here’s a fun little problem: Find three three-digit numbers that use each non-zero numeral once and add up to 999. Follow-up: How many such sets of numbers exist? If you want, take a moment to work on the problem on your own. Then continue reading. Finding a solution For the first question, any set of…
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An interesting question on the G+ Mathematics community I co-moderate asked about the difference between “numbers” and “numerals”. We wound up discussing this at a party I was hosting (which shows the sort of nerds we are), and this post is born from those discussions and my further thoughts. It seems to me we have…
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[mathjax]This is the formula for the circumference of a circle: \[C = 2\pi r\] It’s very simple. My recollection of how it was taught is as a mystical relationship between \(\pi\) and the circumference, as if it were some magical truth that \(\pi\), of all numbers, would be the number that would satisfy the need…
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[mathjax]One basic concept in mathematics that I see students struggle with, and with which I struggled myself, is the notion of expressions. However, when we remove the mathematical component, we can see that expressions behave much like a concept that natural language speakers deal with fairly easily. So let’s start there, in natural language. You…
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[mathjax]In my previous post, I tackled this problem: Try to express positive integers in terms of the sum of two or more consecutive positive integers. For instance, 3 = 1+2, 9 = 2+3+4, and so on. For which numbers 1 to 25 is it possible to do this? I incorrectly concluded that there were no…
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[mathjax]Edit: The bit about the larger prime numbers was due to an error in my VBA programming, but it lead to a better understanding of the problem. Don’t take this article as “final”, is the point. This week’s puzzle in my Mathematics Reasoning class: Try to express positive integers in terms of the sum of…
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[mathjax]In our Mathematical Reasoning class tonight, we discussed this problem: Can your age in years be written in terms of the difference of two square numbers? If so, what two numbers? There are at least three mathematical problems contained here: Given a specific whole number (0 or a positive integer), attempt to find two square…
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[mathjax]One of my concerns as an educator is the way in which peccadilloes of mathematical notation can get in the way of understanding. In the case of logarithms, this has become more troublesome as general education about numeric bases at the secondary level has apparently evolved primarily into an interest of computer programmers. The notation…