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, \[{ \color{orange}9}87456321 รท {\color{orange}9} = 109717369.\] Will this method always result in an integer?
by
Brack harmon
True or False?
If \((a-b) \times (a-b) = (c-b) \times (c-b),\) 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.
by
Vaibhav Priyadarshi
A white square is inscribed in a blue circle, which is inscribed in a larger orange square.
Which area is larger, orange or blue?
by
Chung Kevin
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.
by
Rohit Gupta
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.
by
Agnishom Chattopadhyay