12 of 360 Items .... Type: Puzzle

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On a square lattice, a circle can pass through 2, 3, or 4 points, as in the diagram below. The original question asks for a circle that passes through 5 points, but can you define a circle that passes through other numbers of points? and explain how the circle was created?

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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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If the time is 10:10, what is the exact angle between the minute hand and hour hand?

How about 7:30?

How about 7:35?

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Normally, I'm glad when the media talks about math, even if it is simply the latest "Super-Hard problem from Asia that All of Us Stupid American Adults and Brits Won't be Able to Solve but Their 8 Year-old Do Routinely."

Throw in "I gave it to a mathematician and he couldn't solve it either" and you've got an instant viral hit, apparently.

All right, rant over.




What's the error?

Oh, and solve it if you want, too. It's not really that hard. Further questions:

• Which blanks CANNOT have a prime number in them?


• Which blanks COULD have certain prime numbers?


• Which blanks essentially force this problem to be non-unique?

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What are the values of the letters that will allow you to go as far as possible?

How high can you go?

Is there a better way to solve this than just marching up the line, and guessing at the values for H, R, then for F, U, then for I, V and so on?

The original is below. Is this the best set of values?

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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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Mr Smith has two children. One of them is a boy. What is the probability the other child is also a boy?

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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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You can see that the spider has followed a line around the inside of the box.In the second image, the student has "unfolded" that box and drawn a template.

Is there a way to draw the template so that the spider's path will be one connected path on the unfolded template?

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Weights 1lb through 6lbs.

Where should we start?