Difference between revisions of "2024 SSMO Relay Round 4 Problems"
(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 <...") |
|||
| Line 17: | Line 17: | ||
a+b &= -c,\\ | a+b &= -c,\\ | ||
a^3 - abc &= 4,\text{ and }\\ | a^3 - abc &= 4,\text{ and }\\ | ||
| − | <math>^3 - abc &= T.\\ | + | <math>b^3 - abc &= T.\\ |
\end{align*} | \end{align*} | ||
Then, </math>abc - c^3 = x.<math> Find the value of </math>x.$ | Then, </math>abc - c^3 = x.<math> Find the value of </math>x.$ | ||
[[2024 SSMO Relay Round 4 Problems/Problem 3|Solution]] | [[2024 SSMO Relay Round 4 Problems/Problem 3|Solution]] | ||
Revision as of 15:09, 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 }\\
$b^3 - abc &= T.\\
\end{align*}
Then,$ (Error compiling LaTeX. Unknown error_msg)abc - c^3 = x.
x.$
Solution
