PROBLEM OF THE WEEK #14

Suppose two new mathematical operations have been invented called * and ▲.

If a * b = a + b + b and

a ▲ b = a + a – b,

How much larger is 6 * 4 than 6 ▲ 4?

PROBLEM OF THE WEEK #12

What is the difference between

the sum of all the even counting numbers less than 101 and the
sum of all the odd counting numbers less than 101?

PROBLEM OF THE WEEK #10

PROBLEM OF THE WEEK #8

Two apples weigh the same as a banana and a cherry. A banana weighs the same as nine cherries. How many cherries weigh the same as one apple?

Problem of the week #6

A cooperative farm has three subdivisions, A, B, and C. The subdivisions loan equipment to each other as needed. In the beginning, A loaned B and C as many reapers as each (meaning B and C) then had. Several months later B loaned A and C as many reapers as each (meaning A and C) then had. The following spring C loaned A and B as many reapers as each (meaning A and B) then had. Each subdivision then had 16 reapers. How many reapers did each have to begin with?

Problem of the Week #4

What is the ones’ digit of the product when one hundred 7s are multiplied?

Problem of the Week #2

At a new junior high school, there are exactly 1000 students and 1000 lockers. Lockers are numbered in order from 1 to 1000. On April Fool’s Day the students played the following prank. The first student to enter the building opened every locker. The second student closed every locker that had an even number. The third student changed every third locker, closing those that were open and opening those that were closed. The fourth student changed every fourth locker, and so on. After all 1000 students passed through the locker room, which lockers were open?