Monthly Archives: May 2025

Algebra Challenge – 2025/05/31

Posted on May 31, 2025 by kevin

Let $P(x)$ is a polynomial with integer coefficients so that $P(d)=\dfrac{2025}{d}$, where $d$ is a positive divisor of $2025$. Find $P(x)$.🔑 Claim: There is no $P(x)$ to satisfy $P(d)=\dfrac{2025}{d}$, where $d$ is a positive divisor of $2025$. Lemma: If $P(x)$ … Continue reading →

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Combination Challenge – 2025/05/10

Posted on May 10, 2025 by kevin

Nine light bulbs are equally spaced around a circle. When the power is turned on, each of the nine light bulbs turns blue or red, where the color of each bulb is determined randomly and independently of the colors of … Continue reading →

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Algebra Challenge – 2025/05/03

Posted on May 3, 2025 by kevin

Let $n$ be the real number. Define $[n]$ be the integer part of $n$, and $\{n\}$ be the decimal part of $n$. Solve the following equations: $$\begin{array}{ccccccc} \{x\} & + & [y] & + & \{z\} & = 2.9\\ \{y\} … Continue reading →

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