Category Archives: Logic

2020 Mathcounts State Sprint Round #30

Posted on April 22, 2021 by kevin

Hank builds an increasing sequence of positive integers as follows: The first term is 1 and the second term is 2. Each subsequent term is the smallest positive integer that does NOT form a three-term arithmetic sequence with any previous … Continue reading →

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Cyclic System of Equations

Posted on April 11, 2021 by kevin

Find $abc$. $$ \begin{array}{ll} a+\dfrac{1}{bc} = \dfrac{7}{6}\\ b+\dfrac{1}{ca} = \dfrac{7}{3}\\ c+\dfrac{1}{ab} = \dfrac{7}{2} \end{array} $$ Solution Multiply the first equation by $bc$, the second by $ca$, and the third by $ab$: $$ \begin{array}{ll} abc+1 = \dfrac{7}{6}bc\\ abc+1 = \dfrac{7}{3}ac\\ abc+1 … Continue reading →

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Problem of the Day – April 1, 2020

Posted on April 1, 2020 by kevin

Each of the following statements is true or false. (a) statements (c) and (d) are both true (b) statements (d) and (e) are neither wrong (c) statement (a) is true (d) statement (c) is false (e) statements (a) and (c) … Continue reading →

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Who is the thief?

Posted on February 3, 2020 by kevin

Four burglary suspects, A, B, C, D were summoned to the court to face the judge. When the judge asked: “Who is the thief?”, each of the suspects answered as following: A: B is the thief.B: C is the thief.C: … Continue reading →

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