Difference between revisions of "2024 SSMO Relay Round 4 Problems"
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| Line 17: | Line 17: | ||
a+b &= -c,\\ | a+b &= -c,\\ | ||
a^3 - abc &= 4,\text{ and }\\ | a^3 - abc &= 4,\text{ and }\\ | ||
| − | + | b^3 - abc &= T.\\ | |
\end{align*} | \end{align*} | ||
| − | Then, < | + | Then, <math>abc - c^3 = x.</math> Find the value of <math>x.</math> |
| + | |||
[[2024 SSMO Relay Round 4 Problems/Problem 3|Solution]] | [[2024 SSMO Relay Round 4 Problems/Problem 3|Solution]] | ||
Latest revision as of 15:11, 2 May 2025
Problem 1
Freddy the Frog can jump 
unit right or up. He is at 
and wants to get to 
. However, he is scared of points 
and 
and will not hop onto those points. How many ways can he reach his destination?
Problem 2
Let 
Regular octagon 
is perfectly inscribed within Circle 
. Circle has area 
. If the area of octagon is 
for squarefree 
find 
Problem 3
Let Given that:
\begin{align*}
a+b &= -c,\\
a^3 - abc &= 4,\text{ and }\\
b^3 - abc &= T.\\
\end{align*}
Then, 
Find the value of 
