Last summer my two older brothers and I took a long vacation trip, driving through many states of our great country, sightseeing along the way. We took turns doing the driving for the 2,268 miles. The amount of time that each of us spent at the wheel came out to be in the ratio of [...]
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trottermath
My mother once taught in a small country three-room schoolhouse, where students of different age levels often had to study the same course together. For the course in American History, the kids in the 6th, 7th, and 8th grades were combined into one class. This means that their ages were between 10 and 14. If [...]
Andrew the Assured, Brian the Big, Casey the Careful, Dootles the Dreamy and Edwina the Eager are all members of a reading club, ‘The Burping Bookworms’. They have a bizarre rule in the club: for each 5-person group, they must read 5 books in week, but in a special way–after they finish reading each book [...]
Maximillian Smith is a modern painter of murals. His preferred size of designs are those painted on large rectangles whose length-to-width ratio is 2-to-1. Two of his recent works of art have a unique mathematical connection with his daughter, Mindy, who became a for-real teenager just last year. You see, the numerical difference in the [...]
It is well known by all math students that is an irrational number. This means in simple English that its decimal form, which begins 3.141592…, goes on forever without any repeating blocks of digits. To celebrate Pi Day this year – March 14, or 3/14 – we propose the following problem. Beginning with the “decimal” [...]
Let’s define a function over the non-negative integers in the following manner: P(n) = n when n is a one-digit integer. P(n) = the product of all the digits of n when n > 9. Example: P(1729) = 126, because 1 × 7 × 2 × 9 = 126. Evaluate the following: Note: this problem was shared to [...]
Arthur has invented a new puzzle to show his friends. He calls it: Arithmogons. He draws the following diagram first. Then he puts any three integers he likes in the circles. In the squares he puts the sum of whatever two integers appear on the ends of the corresponding side. Before showing this to a friend, [...]
While taking a coffee break, my secretary, Sue, happened to glance at her digital watch. It showed the following time: 1 : 4 4 “That’s rather curious,” she thought. “If I remove the two dots, I’ll have the number 144, which is the square of 12. I wonder how likely that sort of thing happens [...]
A popular problem in mathematics classes about problem solving concerns finding the unit’s digit of a large power of a number. An example of this might be: Find the unit’s digit of 24000. Of course, the student solving this is not expected to compute 2 used as a factor 4000 times. The reasons should be obvious. [...]
I have three younger brothers, whose names are (in order by age) Gary, Corky, and Steve. Though we have our natural differences, we do agree on one thing: we love to eat salted peanuts while watching football on TV!One Sunday I brought out a big bag of delicious salted, roasted peanuts to share with them. [...]