POTW #24

Consider, if A and B are any integers, then A@B = A – B + 1.

For example 9@3 = 9 – 3 + 1 = 7.

(a) Find 3@(2@4).

(b) Does 3@(2@4) = (3@2)@4?

PROBLEM OF THE WEEK #22

PQRS is a square. Imagine that it can be folded.

P is folded onto Q.

Then Q. is folded onto R.

If the perimeter of PQRS is 2,

what is the perimeter of the new figure?

PROBLEM OF THE WEEK #20

Write the following expression as a simple fraction in lowest terms.

PROBLEM OF THE WEEK #18

Ivanov, Jacobowski, Lebedev, and Malinkov are an architect, composer, dancer, and singer.

Ivanov and her husband invited the composer and his wife to dinner. The dancer said that he enjoyed playing chess with Lebedev. The singer complimented Malinkov on her excellent recipe for cabbage soup. What is the occupation of each person, and is that person male or female?

PROBLEM OF THE WEEK #16

Of a group of 30 high-school students, 8 study French, 12 study Spanish, and 3 study both French and Spanish. How many students of the group study neither French nor Spanish?

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?