Intelligence Correlate

What is the maximum number of coins that equals thirty-two cents using only dimes, nickels, and pennies, and includes each type of coin at least once?

Consider the following two statements: all farmers who are also ranchers cannot come near town; and most of the ranchers who are also farmers cannot surf. Which of the following statements MUST be true?

If every corner of a triangle drawn inside a square touches either a corner or side of that square, what is the difference between the maximum and minimum number of distinct compartments that can be created?

In a random twelve day period, what is the difference between the maximum and minimum number of regular week days?

For every four steps taken forward in a particular direction, a man falls back one step. How far is this man from his starting point if he takes seven steps north, one step south, eight steps east, three steps west, and five steps south?

Assume the following statements are true: Blue and Green make Red; Red and Purple make Yellow; and Black and White make Green. Which of the following color mixes produces the proper resulting color?

What is the maximum area in square feet of a rectangle with a perimeter of forty feet?

An ancient culture built a pyramid with four sides (plus the bottom) and four levels, and the entire pyramid consists of thirty equally sized cubes. How many of the cubes are not exposed at any of its faces?

(Based on an old favorite!) Four numbers, one, two, three, and four, must cross a river with only one raft according to three rules: 1) only number four can operate the raft; 2) no more than two numbers can cross together; and 3) the product of the numbers left behind must be odd.

What is the minimum number of trips in any direction that will transport all four numbers?

How many distinct volumes are created when a hollow octahedron (eight-sided, 3-dimensional figure) is inscribed within a sphere?