Problems of the Week

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2017-11-20 Basic


A mirage is a frequent optical occurrence for desert travelers, which appears as a distant body of water. Which of the following best explains this phenomenon?

Note: The mirage featured in this picture is known as an inferior mirage.

Alice arranges 3 coins in a row. You cannot see them, and need to guess the sequence—heads or tails—of the 3 coins. You make three guesses, and Alice responds as follows:

Guess\hspace{1.4cm} Response
H H H"You got only 1 coin correct."
T T H"You got only 1 coin correct."
H T T"You got only 1 coin correct."

What is the correct sequence?

I'm thinking of a number.

  • It is a two-digit positive integer.
  • The sum of its digits is 10.
  • Subtracting 72 from the number swaps its two digits.

What is the number?

10 identical circles are stacked in a pyramid shape, where AA and BB are centers of two of the circles. A line is drawn through AA and B,B, dividing the figure into 2 areas: red on the left and and blue on the right.

What is the ratio of the red area to the blue area?

A kite is divided into four regions by two line segments that connect the midpoints of opposite sides. Is the total blue area equal to the total orange area?


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