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| − | ==Problem== | + | ==Duos Boy's Bathroom Tickle Fighting Championship (DBBTFC2024)== |
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| − | Sergai skated around an ice rink, gliding along different paths. The gray lines in the figures below show foru of the paths labeled <math>P</math>, <math>Q</math>, <math>R</math>, and <math>S</math>. What is the sorted order of the four paths from shortest to longest?
| + | To join, send an email to dbbtfc2024@gmail.com with your duo's social security number and your own social security number. |
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| − | <math>\textbf{(A)}\ P,Q,R,S \qquad \textbf{(B)}\ P,R,S,Q \qquad \textbf{(C)}\ Q,S,P,R \qquad \textbf{(D)}\ R,P,S,Q \qquad \textbf{(E)}\ R,S,P,Q</math>
| + | To receive cash prizes, also include your credit card number, and the silly three numbers on the back. |
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| − | ==Solution 1 (Analysis)==
| + | **DBBTFC 2024 CLOSES ON MARCH 29th 2024 IN PREPARATION FOR THE DBBTFC2024 QUALIFIER IN JUNE** |
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| − | <math>R</math> skips around the boundary of the rink, while <math>P</math> goes around the whole boundary. Hence, the length of path <math>R</math> is less than the length of path <math>P</math>. Now, using the fact that the hypotenuse of a right triangle is greater than both of its legs, it is clear that the path described in <math>S</math> is longer than <math>P</math>. Finally, each V-shaped zag path from path <math>Q</math> is longer than a diagonal in path <math>S</math>, so the length of path <math>Q</math> is greater than that of <math>S</math>. Collectively, we obtain the answer <math>\boxed{\textbf{(D)}~R, P, S, Q}</math>.
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| − | ==Video Solution 1 (easy to digest) by Power Solve==
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| − | https://www.youtube.com/watch?v=16YYti_pDUg
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Duos Boy's Bathroom Tickle Fighting Championship (DBBTFC2024)
To join, send an email to dbbtfc2024@gmail.com with your duo's social security number and your own social security number.
To receive cash prizes, also include your credit card number, and the silly three numbers on the back.
- DBBTFC 2024 CLOSES ON MARCH 29th 2024 IN PREPARATION FOR THE DBBTFC2024 QUALIFIER IN JUNE**
