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2024 SSMO Relay Round 4 Problems

Revision as of 15:09, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem 1== Freddy the Frog can jump <math>1</math> unit right or up. He is at <math>(1,1)</math> and wants to get to <math>(7, 4)</math>. However, he is scared of points <...")
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Problem 1

Freddy the Frog can jump $1$ unit right or up. He is at $(1,1)$ and wants to get to $(7, 4)$. However, he is scared of points $(3, 1)$ and $(3, 2)$ and will not hop onto those points. How many ways can he reach his destination?

Solution

Problem 2

Let $T = TNYWR.$ Regular octagon $OLYMPIAD$ is perfectly inscribed within Circle $Q$. Circle $Q$ has area $T\pi$. If the area of octagon $OLYMPIAD$ is $a\sqrt{b},$ for squarefree $b,$ find $a+b.$

Solution

Problem 3

Let $T = TNYWR.$ Given that: \begin{align*} a+b &= -c,\\ a^3 - abc &= 4,\text{ and }\\ $^3 - abc &= T.\\ \end{align*} Then,$ (Error compiling LaTeX. Unknown error_msg)abc - c^3 = x.$Find the value of$x.$ Solution

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