Puzzles

The Puzzler of the Month Contest is currently on hold. Please take a look at our Puzzle Archive for past puzzles and solutions.  

View Solvers   View Solution A circle of radius 3 is lowered into the parabola with equation $y=1+4x^2$ until it comes to rest as shown in the figure below.  Determine the exact coordinates of the center of the circle. *You must include sufficient work to support your answer* 

View Solvers   View SolutionThe mean, median, mode, and range of a collection of ten integers are all equal to 10. What is the largest possible number that could be in this collection of integers? Recall: The mean of a set of N numbers is the sum of the numbers divided by N. The median of a […]

View Solvers   View Solution Jack and Elsa are in the process of shoveling their driveway which is 12 feet wide and 24 feet long.  Using two different sized shovels, each of them began in one corner and proceeded to clear a straight path to the opposing corner.  Their paths are shown in the figure below.  […]

View Solvers   View Solution In the figure below, the diameters of two semicircles lie along the diameter of a larger semicircle.  The two smaller semicircles are tangent to one another and the sum of the lengths of their diameters is equal to the length of the diameter of the larger semicircle.  At the point where […]

View Solvers   View Solution You are equipped with two 2’s, two 3’s, and the ability to combine them using addition, subtraction, multiplication, division, and exponentiation. Your job is to create all of the integers from 0 to 36. You may use any number of parentheses to control the order of operations and when possible, all four […]

View Solvers   View Solution Both of the diagrams below include “nodes” connected by edges.  Two nodes that are connected by an edge are said to be “adjacent”.  For each diagram, place the integers 1, 3, 5, 7, 9, 11, and 13 in the nodes so that the positive differences between each pair of adjacent nodes […]

In this puzzle, your goal is to divide the grid into rectangles in such a way that each rectangle contains a single number and that number must designate the number of cells comprising its rectangle.  A sample solution for a much smaller puzzle is shown to the right.   Can you solve this puzzle?    View […]

View Solvers   View Solution The figure to the right (or below, depending on the device you are viewing this on) shows a “polar grid”.  Within this grid, there are several “polar rectangles”.  These polar rectangles are four-sided objects formed by a pair of circular arcs and a pair of line segments.  Examples of these polar rectangles […]

View Solvers   View SolutionA large jug contains 2018 nickels and 2019 dimes.  Next to the jug is a large pile of dimes (treat it as an unlimited number of dimes).  The following procedure is to be performed repeatedly until a single coin remains in the jug.  Two coins are chosen at random from the jug: […]