Answer to the Problem of the Week
for the week of February 20, 2006
Contributed by Bill Funk

The Pill Problem

Bill uses a seven-day pill container to keep track of his daily consumption.   On the day after his pill container is empty, he doles out eight days worth of pills, seven days worth to go into his pill dispenser and the eighth day to take with breakfast.

Bill and his wife have a housekeeper who comes in every other Tuesday to do some light housework for them.

If Bill filled his pill dispenser this Tuesday, February 21, 2006, on the same day that the housekeeper came to work, when will the next date be that she will be here and his pill dispenser will be full?



 

Solution to the Problem:

The answer is 56 days from February 21, or on April 18, 2006.

Bill fills his pill dispenser every eight days.   His housekeeper comes every fourteen days.   The next time that she will be there when his dispenser is full is the least common multiple of 8 and 14, which is 56.



Correctly solved by:

1. Keith Mealy Cincinnati, Ohio
2. Sagar Patel Columbus, Georgia
3. Walt Arrison Philadelphia, Pennsylvania
4. Kshitij (Chris) Mehrotra Elgin, Illinois
5. David & Judy Dixon Bennettsville, South Carolina
6. Kunal Singh Kendriya Vidyalaya
Happy Valley, Shilong, India
7. Emily Powell Winchester, Virginia
8. Tristan Collins Virginia Tech
Blacksburg, Virginia
9. Tobi Kuforiji Columbus, Georgia
10. Magdy Essafty Alexandria, Egypt
11. James Alarie University of Michigan -- Flint
Flint, Michigan
12. Shaan Arora Columbus, Georgia
13. Avery Acuff Columbus, Georgia
14. Danny Gordon Columbus, Georgia
15. Garrett H. Hix Columbus, Georgia
16. JOHN MANCARELLA ----------
17. Lauren Coles Chelmsford, Massachussetts
18. Austin Ball Columbus, Georgia
19. Sarah Taylor Loudoun County, Virginia
20. Russell Beaty Columbus, Georgia
21. Julianne Harris Winchester, Virginia
22. Emily Stapp Mountain View, Wyoming
23. Carter Galbraith Columbus, Georgia
24. Sharina Smith Newport News, Virginia
25. John Spencer Columbus, Georgia
26. Kerry Barwick ----------
27. Neal Amos Columbus, Georgia
28. Nicholas Caligaris Columbus, Georgia
29. Laura Gronauer Winchester, Virginia
30. Tom Walters Mountain View, Wyoming
31. Bharvi Desai Columbus, Georgia
32. Ben Bassett Sewell, New Jersey
33. Justin Fernicola Columbus, Georgia
34. Noel Register Mountain View, Wyoming
35. Praveen Nandamuru Columbus, Georgia
36. Liz Blackwell Harrisonburg, Virginia
37. Maggie Morrison Winchester, Virginia
38. Rachel Pridgen Columbus, Georgia
39. Yassee Pirooz Harrisonburg, Virginia
40. Roni Egley Mountain View, Wyoming
41. Chantel Walker Mountain View, Wyoming
42. Amber Micheli Mountain View, Wyoming
43. Kelley Kolar Winchester, Virginia
44. Matt Arnsbrak Winchester, Virginia
45. Amanda Corsnitz Winchester, Virginia
46. Stephen O'Hara Winchester, Virginia
47. Lauren Ko Winchester, Virginia