Mama Squirrel found a bag of nuts in the driveway of the house near her tree home. She decided to separate the nuts into equal portions for her children.When she tried putting 6 nuts on each plate, one squirrel baby was left out and received no nuts at all. (So there was one sad little [...]
If you were solving AlgPoW problems from the Math Forum in the year 2001, and in particular the one titled “The Professors’ Primes“, (May 7) you met three of my favorite university professors: Drs. Ken Travers, Peter Braunfeld, and Wilson Zaring. Before I left them to finish their lunch in the cafeteria that day, I inquired [...]
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 [...]
Two positive numbers are such that their difference is 7 and the difference of their squares is 105. What is their sum? Your task: 1. Show your kid brother (or sister) what this means by solving it in an arithmetical manner. Be patient. 2. Show your parents how much you’ve learned in Algebra 1 this year by [...]
When I see a good problem somewhere, I like to investigate its properties further and deeper, with the intention of using it to develope problem solving skills in my students. Such was the case when I saw the two problems that you will see in this page of WTM. I hope you will agree with me that they can [...]
INTRODUCTION Before we can explain what a happy number is, you have to learn a new idea, called “recurrent operations.” As the word “recur” means “to happen again”, a recurrent operation must mean a mathematical procedure that is repeated. A very simple example would be the rule “add 5 to the result”. If we started [...]
[Note: In another article we presented the concept of Perfect Numbers, and the related two classes of numbers, Deficient and Abundant. If you have not read that one, it would be a good idea to do so now before proceeding here. The topic before us now is a natural extension of that article.] For centuries [...]
How many perfect people do you know? Or, better, how many perfect people have lived in this world of human beings? Not many, I’m sure you all would agree. Well, the same is true, in a relative sense of the word, in the world of numbers. The ancient Greeks, who held a great reverence for [...]
The basic concept needed to solve this problem is that of the digit sum of a number. The digit sum of a number is nothing more nor less than the “sum of the digits of a given number.” For example, the digit sum of 283 is 2 + 8 + 3, or 13. To make [...]
Problem Set I Separate each group of numbers into TWO smaller groups so that the sum of the numbers in each of the small groups is the same. NOTE: there may be more than one way to do a problem. If so, can you find the other ways? a) {3, 7, 9, 13} f) [...]