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, [...]
I have a quartet of integers with which I’ll present a little number problem for you to solve. Here are some facts to work with: Twice the first integer, minus the second, equals 7. Twice the second integer, minus the third, equals 4. Twice the third integer, minus the fourth, equals 3. Now there are [...]
In Mother Goose City, the most elegant restaurant where the elite meet to eat is the Rub-a-dub-dub Restaurant. It is owned and operated by those three wild and crazy guys: the butcher, the baker, and the candlestick maker. (Perhaps you will recall, they often traveled by tub!) When they decided to become partners in this [...]
In July of 2003, WTM had the good fortune to make acquaintance with a very creative mathematician by the name of Jerry Levy. Mr. Levy was attracted by a certain problem based on a popular theme in recreational math, namely pandigitality. Now, pandigitality is a new word not likely to be in the dictionaries yet, [...]
At the start of a new grading period, Ms. Zhong likes to present her pre-algebra class with extra challenging research problems. One time she wrote the following expression on the chalk board: (A/B)^C + (D/E)^F + (G/H)^I Then she turned to the class and said: “In this expression you are to replace the variables with [...]