Problems of the Week

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2018-04-30 Basic


What explains the motion of the hourglass?

Order the shapes from lightest to heaviest.

a(a21)=2b2 {\color{#3D99F6}a}\big({\color{#3D99F6}a^2}-1\big) = 2{\color{#D61F06}b^2}

If aa and bb are positive integers, is there a solution that satisfies this equation?

On a foreign island, there are three islanders.

One is lying and the other two are telling the truth. One is named Dario and another is named Jean.

Who is Jean?

After letting my large rectangular brownie cool, I found someone had cut a smaller rectangular piece out of the middle. What's worse, they didn't bother to cut it parallel to the sides of the pan!

Is it possible to use a single straight cut to split the remaining brownie into two pieces of equal areas?

Note: The cut can pass through the already cut portion but must be done only from above.


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