Problems

  • Recent Problems

    The 8 × 8 grid at left represents an ocean with a hidden fleet of ships. Ten ships are hidden within the grid — 1 battleship, 2 cruisers, 3 destroyers, and 4 submarines.          

    Each ship may be oriented horizontally or vertically within the grid such that no ship touches another ship, not even at a corner. The numbers along the right and bottom of the grid show how many squares in each row and column are occupied by ship segments. As a start, one square in the grid shows the location of one end of a ship, and the X indicates a square that contains only water (no ship).

    Can you determine the location of all 10 ships?

    Problems

    A problem encountered early in life by the great mathematician and physicist Joseph Fourier was to draw 17 lines that intersect in precisely 101 points. Can you find a way to do it? 

    (Fourier was able to find four families of solutions to this problem.)

     

    Problems
    A grocery store sells brown rice in 3-pound bags and white rice in 5-pound bags. Katrina bought a total of 22 pounds of rice. How many bags of rice did she buy?
    Problems
    Grades: 6th to 8th, 9th to 12th
    Expression/Equation
    Algebra
    Analyze and solve linear equations and pairs of simultaneous linear equations.
    Reasoning with Equations and Inequalities
    Creating Equations
    8.EE.C.8b, HSA-CED.A.3, HSA-REI.C.6, 8.EE.C.8c

    The Fibonacci sequence is shown below, with each term equal to the sum of the previous two terms. If you take the ratios of successive terms, you get 1, 2, \frac{3}{2} , \frac{5}{3} , \frac{8}{5} , \frac{{13}}{8} , and so on. But as you proceed through the sequence, these ratios get closer and closer to a fixed number, known as the Golden Ratio.

    1, 1, 2, 3, 5, 8, 13, …  

    Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?

    Problems
    Grades: 6th to 8th, 9th to 12th
    Ratio & Proportion
    Functions
    Stats & Probability
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Interpreting Functions
    Investigate patterns of association in bivariate data.
    Understand ratio concepts and use ratio reasoning to solve problems.
    6.RP.A.1, 8.SP.A.1, HSF-IF.A.3, 7.RP.A.2a

    Three puzzle competitors are blindfolded. A white piece of paper is glued to each one’s forehead and they are told that not all the pieces of paper are black. The blindfolds are removed and the prize goes to the first man to deduce whether the paper on his forehead is white or black.

    All three announce white at the same time. Why?

    Problems
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