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    Challenging Math Problems
    Challenging Math Problems
    Challenging Math Problems
    Ebook103 pages1 hour

    Challenging Math Problems

    By Terry Stickels

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    About this ebook

    "Fun and highly formidable math problems and puzzles from noted puzzle creator Terry Stickels." — Window on Resources
    Two friends wish to meet for breakfast twice a month throughout the year. In how many ways can they choose those two days so that they never meet on consecutive days?
    You want to measure 30 seconds and you have two pieces of string, each of which burns for 40 seconds. How can you accomplish this without bending, folding, or cutting the strings?
    A positive whole number is divisible by 3 and also by 5. When the number is divided by 7, the remainder is 5. What is the smallest number that could work?
    These are but a few of this book's assembly of the most challenging puzzles imaginable ― and they require no background in higher math, just good thinking skills. Terry Stickels, a well-known puzzle-maker, has compiled 101 of some of the best and most entertaining problems ever published. All of the challenges, which range from probability puzzles to dice games, have two things in common: each offers the "Aha!" moment of discovery that puzzle-solvers love, and they're all fun. Complete solutions for all puzzles explain every detail.

    LanguageEnglish
    PublisherDover Publications
    Release dateOct 21, 2015
    ISBN9780486808574
    Challenging Math Problems

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      Book preview

      Challenging Math Problems - Terry Stickels

      www.terrystickels.com

      PUZZLES

      1

      If a teacher can place his students eight to a bench, he will have only three students on the final bench. If he decides to place nine students on a bench, he’ll have only four students on the final bench. What is the smallest number of students this class could have?

      2

      Here’s a probability puzzle that may test even some of the best mathematicians.

      Imagine you have two opaque boxes. One box has one white marble and the other box has one white marble and one black marble. Of course, you can’t see into either box. Simultaneously, you reach into both boxes, grab one marble from each, and quickly switch the marbles without looking at them. You then pick one of the marbles from one of the boxes. What is the probability the marble you pick is white?

      3

      Molly places 200 kilograms of watermelons in cases in front of her shop. At that moment, the watermelons are 99% water. In the afternoon, it turns out that it is the hottest day of the year, and as a result, the watermelons start to dry out. At the end of the day, Molly is surprised because she wasn’t able to sell a single watermelon, and the melons are now only 98% water. How many kilograms of watermelons does Molly have left at the end of the day?

      4

      One of the most interesting studies in mathematics is the way numbers grow as they approach infinity. So, for this puzzle consider if you were to take the limit, as "n approaches infinity, put the following in order, going from lowest to highest in value. Note: c is any positive integer you choose greater than 1. All values of n" are positive and greater than one.

      5

      What number comes before the 3 to start this sequence?

      ? 3 11 31 75 155 283 471

      6

      A positive whole number is divisible by 3 and also by 5. When the number is divided by 7, the remainder is 5. What is the smallest number that could work?

      7

      What are the missing digits in the division below? All the 3s are given. The placeholder Xs may be any digit from 0 – 9, excluding 3.

      8

      In the figure below, the total area of rectangle BCDE plus triangle ABE is 192 sq. units. What is the length of AB?

      9

      The mean of three numbers is 12 more than the least of the numbers and 18 less than the greatest. The median of the three numbers is 9. What is the sum of the three numbers?

      10

      Alison and Amelia live 14 miles apart. Alison started to drive her car toward Amelia’s house. At the same time, Amelia started to drive toward Alison’s house. When they met, Alison had been driving for three times as long as Amelia and at 3/5 Amelia’s rate. How many miles had Amelia driven when they met?

      11

      On a normal die, the sum of the dots on opposite faces is seven.

      On the four dice above, the opposite faces total seven but one of the pictures is incorrect because of the orientation of the dots. Which die is incorrect? There is enough information from the four views to make this determination.

      12

      Below are 24 matchsticks arranged in a 3 × 3 grid. The circles represent the matchsticks that would have to be removed so that there are no squares of any size remaining in the grid. The minimum number, as you can see, is six matchsticks that need to be removed. There are several ways to accomplish this.

      Now, what is the minimum number of matchsticks that need to be removed in a 4 × 4 grid of 40 matchsticks? Remember, there can be no squares, of any size, remaining.

      13

      For what value K is the following system consistent?

      1)P + Q = 6

      2)KP + Q = 18

      3)P + KQ = 30

      14

      Molly’s yard has twice the area as Mickey’s yard and 6 times as much area as Maggie’s lawn. Maggie’s mower cuts 1/3 as fast as Mickey’s mower and 1/5 as fast as Molly’s mower. If they all start to mow their respective lawns at the same time, who will finish last?

      15

      A factory makes gears for heavy machinery. Because of the intense heat and friction, a solid form of resin sticks is manually inserted into one of the machines at regular intervals to aid the grinding process.

      Each resin stick has enough left over residue so that four pieces of it can be reformed to make another whole new piece of resin. At the beginning of the second

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