Category: Logic

  • Can You Win Pioneer Woman's Big Fat Smartypants Quiz?

    Can You Win Pioneer Woman's Big Fat Smartypants Quiz?

    Well, I sure can’t. Unless I work the numbers.

    I’m a subscriber of Ree. Well, the homeschool part of Ree’s site The Pioneer Woman. And I just got the post titled Big Fat Smartypants Quiz in my email.

    I like to fancy myself as pretty smart. And I’m sometimes more confident that I should be.

    So I took the bait.

    Turns out, the only way I’m going to win this Smartypants Quiz is to work the numbers.

    How do I work the numbers?

    The first step to cheating (and let’s be honest, that’s what this is) is understanding the landscape.

    The questions on this quiz aren’t logical. They’re trivial. Which means you have to be knowledgable, not clever or intelligent.

    There are tons of things I am – but knowledgeable I’m not.

    How many ways can I answer?

    The first two questions are no-brainers. Name and email. Got it.

    Of the remaining 18 questions – 16 have four options. The other two (#14 and #16) are yes/no questions.

    Assuming I know my name and email address, the number of possible responses by one person (me) is

    \(1 \times 1 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 2 \times 4 \times 2 \times 4 \times 4 \times 4 \times 4\)

    Or 17,179,869,184.

    Ouch.

    Which means that the probability of randomly guessing and winning is 0.0000000000582076609.

    That’s, well… pretty small.

    And if I gave it a shot (to randomly guess) it would take 544 years to go through all the options (if I could submit a new answer set every second).

    By that time Ree would have given someone else the iPad and everyone involved would be dead.

    But… can I win anyway?

    No sense in guessing from the start. I’ve already decided that it would take too long. So I need another tactic.

    Thus, I need to know other things about this quiz.

    FACT: I get immediate feedback on what grade I make.

    That might be helpful.

    Doing some testing I can determine that…

    FACT: I get no points for entering my name and email address.

    Seems dumb, I know, but if I get points for name and email, then I have to keep putting them in while I do my experiments.

    There are some things I know!

    I know that the 10th letter in the Greek alphabet is kappa (it’s a math thing), so I go for answering only question #5 and find…

    FACT: I earn 6% for a correct answer on #5, with no other questions answered.

    I remember that Juliet gets mad that Romeo drank all the poison, so I go for #7 as “a dagger.”

    FACT: I earn 6% for a correct answer on #7.

    So it looks like each question (other than name and email) get 6 percentage points. But 18 * 6 = 108. Way more than 100.

    Curious.

    Now I do what all good mathematicians (and cheaters) do. I wonder…

    CONJECTURE: I’ll bet the two yes/no questions are only worth 2 percentage points.

    I recall Katherine Hepburn being married to just about everyone. So I answer “true” to #14. I get ZERO percentage points. So I try again with the opposite.

    FACT: Strangely, my conjecture was wrong. I got all 6% for answer “false” on #14.

    So I do more experiments!

    It takes me less than two hours to experiment and get a 100% on the quiz. Significantly less than 544 years.

    I gave myself the gold star!

    “How can I use this with my kids?” you ask?

    Ah… there’s the kicker!

    Math isn’t just about numbers and books and getting the right answer. Math is about figuring stuff out.

    It’s about wondering, guessing, playing. It’s about conjecturing and getting stuff wrong.

    And it’s sometimes about brute force – getting your hands dirty and finding out what the heck is gonna get you to success.

    Play a game or take a quiz.

    The next time you and the kids have an opportunity to play a game or take a test or quiz, see how you can do it without really doing it. Point out that the logic behind things is really just math.

    And enjoy it!

    Share your thoughts in the comments or on twitter/x.

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  • HELP – Logic Puzzle Announcing The Homeschool Blog Awards

    HELP – Logic Puzzle Announcing The Homeschool Blog Awards

    Okay, y’all, I’m in over my head. I’m trying to create a logic puzzle as a nifty way to announce The Homeschool Blog Awards. Having never created a logic puzzle before, I thought, “How hard can it be?”

    Well, pretty darn hard.

    So I thought I’d put my start out there, as well as the solution, and see if I can get some help from y’all.

    Read the puzzle, try to figure out the solution, then suggest in the comments one or more clues that I should add (or get rid of).

    The Puzzle

    The Homeschool Post is the sponsor of The Homeschool Blog Awards every year. Writers of The Homeschool Post aren’t allowed to win, nor be nominated. So some of the writers of thought it might be fun to do a “within the family” blog award for themselves.

    After all was said and done, they decided to pass all information over to me, the math mom in the team, and let me figure out the winner. Alas, the information wasn’t well organized. So I had to figure out which blog went with which person, who voted for whom and who was the winner.

    The Clues

    Six of the writers decided to participate. They were

    • Lana (like Banana)
    • The writer of OK Homeschool Mom
    • Heather
    • The writer of Knit 1 Kids 4
    • Gidget
    • Rachel
    1. Heather said, “I love everyone. I’m just voting for them all!”
    2. Someone suggested that nobody should vote for themselves. So they agreed on that.
    3. The writer of Finding Joy voted for three people, including Heather and Kristal.
    4. Everyone who voted for Rachel also voted for the blog I Love My 5 Kids.
    5. Everyone but Gidget voted for the author of the blog SprittiBee.
    6. The author of  Homeschooling Unscripted only got two votes.
    7. Donnetta and Gidget got the same number of votes. As did the authors of SprittiBee and Knit 1 Kids 4. Also, Rachel and the author of I Love My 5 Kids had the same number.
    8. The author of Finding Joy is very popular – everyone voted for her.

    The Solution

    Here is the solution of who voted for whom. The initial of the person is on the left and the initial of the people for whom they voted is in the curly brackets. Click on the picture to enlarge.

    Owners/writers of the blogs are here:

    • Donetta publishes OK Homeschool Mom
    • Gidget publishes Homeschooling Unscripted
    • Heather publishes SprittiBee
    • Kristal publishes Knit 1 Kids 4
    • Lana publishes I Love My 5 Kids
    • Rachel publishes Finding Joy

    Don’t forget…

    Suggest a clue in the comments!

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  • Some Fun Ways to Teach Counterexamples

    Some Fun Ways to Teach Counterexamples

    This post is inspired by a discussion with Betty Ann on the www.Teachers.net math chatboard. She writes:

    I’ve got a high school student doing a very basic geometry course. She’s having trouble with the concept of a counterexample. I’m writing a worksheet on counterexamples and would love to have some more simple conjectures for her to work with.

    A counterexample is a special kind of example that disproves a statement. We start using these in Geometry because that’s the first course that really teaches proving things.

    Counterexamples are an essential part of logic.

    They don’t really need to be associated with math (or even philosophy) to be applicable. Which is the cool thing about them.

    Suppose someone says, “I always get to school on time.” It only takes one day when he isn’t on time at school to negate this statement. That one day would be considered the counterexample.

    We do this all the time and never use the fancy math term “counterexample.” So when we teach it, it’s helpful to tap into these everyday uses.

    Counterexamples are everywhere.

    Here are some statements for which students can come up with easy counterexamples.

    In the house:

    • Any four legged piece of furniture is a table.
    • If something has a knob on it, it’s a faucet.
    • Everything in the house with hands is a clock.
    • If a living being has eyes, it’s a human.

    In the grocery store:

    • Everything that costs $2.99 is a gallon of milk.
    • Everything that’s hot is fried chicken.
    • If something is white, then it is mayonaise.

    In the classroom:

    • If it’s a book, it has words. (Make sure there are blank journal books around.)
    • All books teach arithmetic.
    • Anything on the wall is a whiteboard.
    • If it’s full of pencils, then it’s a coffee mug.

    You can make your own statements for counterexamples.

    Choose a noun. Notice a feature about it. Then put it together using this MadLibs format:

    • Everything that has <feature> is a <noun>.
    • All <plural noun> have <feature>.
    • If it <has this feature>, then it’s a <noun>.

    You can also reverse them like this:

    • Every <noun> has <feature>.

    For instance:

    • Every cow is brown.
    • Every lightbulb is 60 watt.
    • Every hammer has a wooden handle.

    Which counterexamples or counterexample building method do you use?