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On this number pad, a nine-digit number is made by walking through each digit once, starting from a random digit and only moving to adjacent digits.
That number is then divided by its first digit. In this example, 987456321÷9=109717369. Will this method always result in an integer?
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True or False?
If (a−b)×(a−b)=(c−b)×(c−b), then it must be true that a=c.
Bonus: If you think it's true, prove it; if you think it's false, find a counterexample.
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A white square is inscribed in a blue circle, which is inscribed in a larger orange square.
Which area is larger, orange or blue?
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Why is a seesaw always tilted to one side, while an empty beam balance is always balanced horizontally?
A. The center of mass of a seesaw is slightly above the hinge point, while that of a beam balance is slightly below the hinge point.
B. The center of mass of a seesaw is slightly below the hinge point, while that of a beam balance is slightly above the hinge point.
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The diagram shows how identical equilateral triangles can be tiled to make a regular hexagon with no leftover tiles.
Which of the following numbers of triangles can also do this?
Regular hexagons can be made with 6 tiles, 24 tiles, and 54 tiles.
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