493: It Sure Would Be Easier

If we are told that we have a quadrilateral inscribed in a circle with diameter 10, do we KNOW if the angle at B and the angle at D are 90°? Because that sure would make it easier to find x.

492: Sneak in Some Algebra

Marilyn Burns pointed out:

Well, does it?
Is there a pattern that always works?


source.

491: Discuss the Errors, part 2

This question is from the NY Regents test, and discussed by Patrick Honner in his long-running series, "Are These Tests Any Good?".

Can your students find what is wrong with it?

How would they fix it?



source.

490: Discuss the Errors, part 1

These questions are from the NY Regents test, and discussed by Patrick Honner in his long-running series, "Are These Tests Any Good?".

Can your students find what is wrong with them?

 

and

source.

489: Which Quadratic Formula?

So ... I've seen a couple of YouTube videos that feature songs about the Quadratic Formula.  I often see it written like this:

$x = \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$

and it occurs to me that I've always written it this way:

$x = \dfrac{-b}{2a} \pm \dfrac{\sqrt{b^2-4ac}}{2a}$

Which one is better?

487: The Fifteen Puzzle

Everyone older than ten knows that there is a way to play tic-tac-toe so that you can never lose. Any game that can be played to a draw unless someone makes a newbie's mistake, is boring once you know the secret.

Let's look at this one and see if you can find a strategy for it:


Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.

Is there a guaranteed winning strategy for Player 1?
Is there a guaranteed winning strategy for Player 2?

source:

Players alternate writing a number from 1 - 9 (once used, it’s dead). First one with a set of three numbers that sum to 15 wins.

— Chris Lusto (@Lustomatical) July 16, 2015

How does his later comment help? "It’s equivalent to tic-tac-toe since any row/col/diagonal in a 3x3 magic square sums to 15, but more mathematically interesting."

486: The Bowling Pins Puzzle

Everyone older than ten knows that there is a way to play tic-tac-toe so that you can never lose. Any game that can be played to a draw unless someone makes a newbie's mistake, is boring once you know the secret.

Let's look at this one and see if you can find a strategy for it:

There are thirteen pins and the two players take turns bowling.When bowling, you can knock down any pin or two adjacent pins (but not two that are separated by a space) that you like.  The loser knocks over the last pin.

The gnome has bowled first, knocking down #2. How do you best play this game so that you are guaranteed to win?

If you go first, what is your best play?

source: Loyd's Encyclopedia, 1914.