Every thirteenth day, Romeo visits the park, hoping to find Juliet
there; every seventeenth day, Juliet does the same, hoping to
find Romeo. They almost met when Romeo visited the park on
Christmas Eve and Juliet went on Christmas Day.
When will they meet?
Solution to the Problem:
The lovers will finally meet on St. Valentine's Day, Feb. 14.
Romeo visits on Dec 24. His next visit (13 days later) is JAN 6, then JAN 19, Then FEB 1, then FEB 14.
Juliet visits on DEC 25. Her next visit (17 days later) is JAN 11, then JAN 28, then FEB 14.
Steven Burak sent in the best mathematical solution:
Set up an equation... 13x - 1 = 17y where x is the number of cycles Romeo waits,
and y is the number of cycles Juliet waits. Isolating for x, we get x = (17y + 1)/13.
Now, we know y must be an integer (because you can't have anything but a whole cycle),
so 17y + 1 must equal a multiple of 13. But y must also be an integer.
The lowest values for which all these conditions will hold is when x = 4 and y = 3.
So 13x = 13*4 = 52.
So 52 days after Christmas eve (or 51 days after Christmas) they will meet. Which is Feb 14.
Correctly solved by:
| 1. Bo Aimone |
Mountain View High School, Mountain View, Wyoming |
| 2. Alyssa Sibelrud |
Mountain View High School, Mountain View, Wyoming |
| 3. James Alarie | Flint, Michigan |
| 4. Chad Fore | Gate City, Virginia |
| 5. Richard Price |
Batley Girls High School, West Yorkshire, United Kingdom |
| 6. Masyra Wilkinson |
Mountain View High School, Mountain View, Wyoming |
| 7. Austin Hale |
Mountain View High School, Mountain View, Wyoming |
| 8. James Nixon |
Mountain View High School, Mountain View, Wyoming |
| 9. bindlh@kpmath.com |
Mountain View High School, Mountain View, Wyoming |
| 10. Math Club | Mount Vernon, Ohio |
| 11. Keaton Flugel |
Mountain View High School, Mountain View, Wyoming |
| 12. Kaylor Dolezal |
Mountain View High School, Mountain View, Wyoming |
| 13. Hannah Black |
Mountain View High School, Mountain View, Wyoming |
| 14. Hayden Meeks |
Mountain View High School, Mountain View, Wyoming |
| 15. Brandon Preston |
Mountain View High School, Mountain View, Wyoming |
| 16. Marissa Vitt |
Mountain View High School, Mountain View, Wyoming |
| 17. Austin Henstra |
Mountain View High School, Mountain View, Wyoming |
| 18. Jenny Harant |
Mountain View High School, Mountain View, Wyoming |
| 19. Karly Horton |
Mountain View High School, Mountain View, Wyoming |
| 20. Crystal Schleichardt |
Mountain View High School, Mountain View, Wyoming |
| 21. Jt Gray |
Mountain View High School, Mountain View, Wyoming |
| 22. Alex Snyder |
Mountain View High School, Mountain View, Wyoming |
| 23. Newt Iorg |
Mountain View High School, Mountain View, Wyoming |
| 24. Caleb Flake |
Mountain View High School, Mountain View, Wyoming |
| 25. Gage Meeks |
Mountain View High School, Mountain View, Wyoming |
| 26. Kayla Burch |
Mountain View High School, Mountain View, Wyoming |
| 27. Josey Pitts |
Mountain View High School, Mountain View, Wyoming |
| 28. Trystin Walker |
Mountain View High School, Mountain View, Wyoming |
| 29. Steven Burak |
Drexel University, Philadelphia, Pennsylvania |
| 30. David & Judy Dixon | Bennettsville, South Carolina |