One of the guards is instructed to kill Spock if he tries to leave through his exit; the other guard is instructed to let him go.

The fourth student does the same to every fourth locker, and so on through 1, students. Sally has three cubes made of modeling clay.

A mysterious box, contents unknown, might weigh anywhere from one to forty pounds, though it definitely weighs a whole number of pounds you don't have to worry about ounces.

Nobody has proved this yet, but that's the way it appears. Draw a bisector through this triangle out to a radius of sqrt 3.

You are given 9 lattice points in 3 dimensional space. The first student walks down the line and opens each one. Take a traditional Battleship game and place 25 pegs in the lower left quadrant, rows F through J and columns 1 through 5. How should he procede to obtain his fly. If it reads 2 ounces you've found the gold, but if it reads just 1 ounce, the gold coins are in one of the other 9 sacks.

Tha table is frictionless of course, and a ball bounces off the side like a mirror, with the angle of incidence equal to the angle of reflection. For instance, if we begin by sending 2 missionaries across, the remaining missionary will be eaten by the 3 cannibals.

Educators might want to present the problem on Friday, let the students think about it over the weekend, and talk about it on Monday. Note, this problem was featured on an episode of Columbo, though it is older than that.

Since the buckets have no measuring lines on them, a "transfer" consists of pouring the entire contents of one bucket into another, or as much as will fit without overflowing. Let's try to construct a party that does not have three mutual friends or three mutual strangers.

The train is traveling at 40 mph. Problem of the Week is now a discussion board that functions similarly to StackExchange. Maybe smaller squares would lead to a solution, or maybe you need to develop a complex pattern of irregular shapes with curved boundaries.

Hint, the floor of the cube looks like a square of squares, as illustrated by the previous problem. Pain the origin red, and designate 2 points orange and yellow on the unit circle, forming an equilateral triangle. At the end, each glass has the same amount of liquid. The ball is launched out of the lower left pocket at some prescribed angle.

The second student closes the even numbered lockers. Find a sequence of 20 moves that leaves a peg in row B. How many different red-blue cubes are there. All four wore hats. How many lockers are open.

The water level is lower after you throw the rock overboard. How about two segments that form two legs of a triangle, like the letter V.

So 90 degrees it is. If cannibals ever out-number missionaries, on either side of the river, they will eat the missionaries, and we don't want that. With a diagonal between 0. First figure out what the total is.

Graeme, a perceptive and intuitive mathematician, gave us for many years math problems that perplexed and delighted visitors. Be warned that many of these problems are not for the faint of heart; some of his solutions are longer than three or four solutions from other problem pages.

Free Math Worksheets, Problems and Practice | AdaptedMindTrack real-time progress · Customized Learning · Measurable Results · Fun Games & PrizesCourses: Counting Coins, Metric Conversion, Factoring, Multiples.

Want to practice with really hard SAT math problems to get a perfect math score? Here are the 13 hardest questions we've seen - if you dare.

The 13 Hardest SAT Math Questions. If you felt these questions were challenging, be sure to strengthen your math knowledge by checking out our individual math topic guides for the SAT.

Fun and Challenging Math Problems for the Young, and Young At Heart. These problems are aimed at junior high and high school students with a flare for mathematics and logic.

Applied Math Actuarial Courses Course Pages Schedules Textbook Listing but he continued to provide the problems. And even now many of the problems appearing in Problem of the Week were provided by Michael Golomb. He created many of the problems himself, and collected (and often modified) the others from various sources.

Challenging math word problems for all levels. A Collection of Math Word Problems for Grades 1 to 6.

Challenging math problems
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Open Middle - Challenging math problems worth solving