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Question: If you have a rope around a soccer ball and the moon, which rope would have to increase in length more to create a one meter gap between the rope and the soccer ball/moon?

Hint: Remember, Circumference = Diameter * π

Answer: They would both increase length by 2 π meters. Since Circumference = Diameter * π, when they increase in length it is true that Circumference = (Diameter + 2) * π. Distribute the π and you get Circumference = Diameter * π + 2 * π.

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Question: If you have a cake, how many pieces of cake can you form with 3 straight cuts?

Answer: 8 pieces. Make two cuts like you normally would then one horizontal cut from the side of the cake.

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Question: A farmer has three fields. One of them has 3 bundles of hay, another has 4, and the last has 5. How many would he have in the first field if he combined all of them in that field?

Answer: Just one, he combined them all.

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Question: Queens can move horizontally, vertically and diagonally any number of spaces as illustrated. One piece 'attacks' another if it moves to the same tile that the other piece is on. How can you arrange eight queens on the board so they cannot attack each other?

Hint: Four must go on black and four on white.

Answer: Here are the two solutions. This is usually solved with guess and check although using logic may be faster. We know that each queen must be in it's own row vertically and horizontally. We also know that 4 of the queens must be on white and 4 on black. This is true because with 4 queens on the same color all of the rest of that color is venerable to attack. (It could be done with math).

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Question: Why does the second shape have an open block when the first shape does not?

Answer: The two triangles have different slopes so in the second shape the two triangles cause the shape to bulge out to account for the extra square unit.

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