Author Archives: kevin

Circles in a Square – Part 6

Posted on December 2, 2019 by kevin

Look at the following figure, a simi-circle is inscribed between the quarter circle and one side of the unit square. What the radius of the semi-circle? Obviously, $G$ is the center of the semi-circle, line $\overline{CG}$ crosses $F$, the tangent … Continue reading →

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Circles in a Square – Part 5

Posted on December 1, 2019 by kevin

Today, we talk about a classic problem of packing circles in a square. Given a unit square, you need to make 3 congruent, non-overlapping circles that are as big as possible. It has been proven that the arrangement of 3 circles must be as the following. Can … Continue reading →

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Circles in a Square – Part 4

Posted on November 30, 2019 by kevin

In the previous post of this series, we asked if the area of the region can be solved without using previous calculation. Look at the figure below, after drawing several lines by connecting several points: The fan area of $[AEF]$ is $\dfrac{\pi}{12}$, because line $\overline{AE}$ and … Continue reading →

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Problem of the Day – November 28, 2019

Posted on November 28, 2019 by kevin

There is a staircase with 13 steps, and you can climb either 1 step or 2 steps at a time. Can you find out the number of unique ways you can climb to the top of the staircase? The order … Continue reading →

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Problem of the Day – November 27, 2019

Posted on November 27, 2019 by kevin

How many 4-digit numbers are there without digit 2 and 3, such as 7450? How many of them are there with at least one digits as 2 or 3, such as 1200, 3401, 1234?

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