Problems of the Week

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2018-04-09 Basic

         

A standard deck with 52 cards—26 red and 26 black—is shuffled.

What is the probability that the top card is the same color as the bottom card?

On a beach, there is a natural, straight shoreline with waves approaching diagonally towards the shore. The arrows indicate the direction of the waves.

A breakwater is placed perpendicular to the shoreline.

After some time, will the shoreline appear more like A or B?

Hint: Waves approaching the shore carry sediment with them.

This 3D solid is colored on each of its 18 faces.

What is the minimum number of colors needed so that no two edge-sharing faces are the same color?

Note: Faces that share a vertex but not an edge can be colored the same.

The minute hand happens to be precisely on top of the hour hand on a traditional analog clock.

Assuming the clock is running normally, what was the angle between the two hands 2 hours and 20 minutes ago?

You have a note from your friend, Papa George, that reads, "Find me if you can! I'm either in the park on Canal Street or the one on Baker Street. I've told my sons which one."

Papa George has identical triplet sons all named George. They are wearing shirts of different colors, as shown. One of them always tells the truth, another always lies, and the other sometimes tells the truth and sometimes lies. You ask the boys which park their father is in, and they respond as shown.

Which park is Papa George in?

Each bubble is a separate statement, and they are said in sequence from top to bottom.

Each bubble is a separate statement, and they are said in sequence from top to bottom.

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