12 of 42 Items .... Course: LOGIC

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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 game 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?

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from NCTM:

How many knots will form if you pull the ends of the string in opposite directions?

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Why did the puzzle creator only ask for circles A and B?

In the diagram, the 19 circles are to contain the integers 1 to 19 once each. The sum total along any of the lines is 38. Determine the integers in circles A and B.

Is it possible to find the rest of the circles, too?

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R3
There are three red hats and two black hats on a hatstand.

Melba, Fran, and Brent line up in a single file line, and the mad Hatter places a hat on each person’s head and tosses the rest into a box where no one can see them.

The Mad Hatter takes off Brent's blindfold. Brent, who could see Fran’s hat and Melba’s hat, says, “I don’t know what color my hat is.”

The Mad Hatter takes of Fran's blindfold. Fran, who could only see Melba’s hat, says, “I heard what Brent said, but I don’t know what color my hat is.”

As the Mad Hatter moved to take off Melba's hat, she said, “I don't need you to take off my blindfold. I know what color my hat is.”

What color is Melba’s hat and how does she know?

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What do you notice?
What do you wonder?

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If you are parked during any part of the time indicated, then you need to pay, even if it's only for a few minutes at the beginning or end of your shopping. (If you only are there for the five minutes between 8:00 and 8:05, you only pay a pro-rated fee.)

If you park at any random time and leave your car there for an hour, are you more likely to pay or more likely to not pay?

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Sam Shah wrote:

Matt Enlow (math teacher in MA) posted a fascinating problem online today, one he thinks of when storing all those plastic bags from the grocery store. You shove them so they all lie in a single bag, and throw that bag under the sink. Here’s the question: how many different ways can you store these bags?

For 1 bag, there is only 1 way.
For 2 bags, there is still only 1 way.
For 3 bags, there are 2 ways.

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Let's use this Rubik's Cube again, shall we? The total surface area of the cube is 54 square units.

• Is it possible to remove a unit cube without changing the surface area?


• How about removing one that increases the area by 2 square units ....


• or maybe one that can be removed that increases area by 4 sq units?

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Suppose that a white Rubik's Cube is painted blue on top and bottom and painted red on the four lateral sides. The cube is then separated into its 27 smaller cubes.

How many unit cubes have at least one red face and one blue face?

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From Talking Math With Your Kids:

"Which shape doesn't belong?" is a question that kids of any age can deal with.Each page has four shapes, any of which can be considered "wrong" for some reason. Challenge your kids to find a reason for why each shape might not belong in the group of four.










Send your sets!

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The day before yesterday Edward was 17. Next year he will be 20. How can that be the case?

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If I were to give you $50 we'd have the same amount. If you were to give me $50 I'd have 9 times as much as you. How much do we each have?