Monthly Archives: November 2019

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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Problem of the Day – November 26, 2019

Posted on November 26, 2019 by kevin

How many 4-digit numbers are there with digits in absolute descending order, such as 8520? And how many 4-digit numbers are there with digits in absolute ascending order, such as 3569?

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Solution to November 25, 2019′s Challenge

Posted on November 26, 2019 by kevin

By connecting various points in the figure, we have the following: It is obvious that the radius of each quarter circle is $\dfrac{\sqrt{2}}{2}$, and the area of two green regions is: $$\dfrac{1}{2}-\dfrac{1}{4}\cdot\pi\cdot(\dfrac{\sqrt{2}}{2})^2=\dfrac{1}{2}-\dfrac{\pi}{8}$$ Therefore, the total area of the blue regions … Continue reading →

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