Problems of the Week

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2017-02-13 Basic


To make the room colors contrasting, Robin decides to paint in such a way that no two rooms connected by a door have the same color.

Here is the blueprint of her house, where she used numerous colors:

Can she achieve her goal using just her two favorite paint colors, red and yellow?

For what value of xx does 10x×1002x=10005?\large 10^{x} \times 100^{2x}=1000^{5} ?

You want to loosen a stubbornly tight screw, and have two different handles available for the screwdriver.

If you apply the same force to both handles below, which handle is easier to turn the screw with? In other words, which handle will generate a greater turning moment for the screw?

Black has made a wrong move. Then it's White's turn to move.

How many moves does White need for the fastest possible checkmate?

The figure above shows a regular hexagon with area 1.

What is the area of the shaded region?


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