December 2011
Problem of the Month

Romeo and Juliet

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.

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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

Send any comments or questions to: David Pleacher