Answer to September 27, 2004 Problem

The Grandchildren Problem

  1. Mr. Pleacher has four grandchildren.
  2. They were born in four consecutive months with the oldest born in the first of the four months, the second oldest born in the second month, and the youngest in the fourth month.
  3. The days on which they were born are ascending numbers from the oldest grandchild down to the youngest (in other words, the oldest grandchild was born on a day which is less than the day that the 2nd oldest child was born, and so on.
  4. Three of the grandchildren were born in Leap Years, but the oldest was not.
  5. Carrie's birthday was on the 18th of the month, and the oldest was born on the 2nd of the month
  6. None of the grandchildren was born in January or July.
  7. The sum of the days on which they were born is 77.
  8. The youngest was born on the 29th of a month which has 30 days.
  9. James was born in 1998.
  10. Kate was born in May
  11. Jackson and one of his cousins were the only ones born in 2004.

Can you give the birthday (month, day, and year) for each of the four grandchildren?

Extra Credit: Can you predict when my next grandchild will be born?

 

Solution to the Problem:

James Mar 2 1998
Carrie Apr 18 2000
Kate May 28 2004
Jackson Jun 29 2004

Extra Credit: My next grandchild will be born on July 30 or 31, 2006 (if all the sequences hold true).
However, one of my daughters sent in the following answer for the extra credit: 2/14/06; and she has more say in the matter than I do.

To solve the logic problem:
1. The names were given in the puzzle.
2. You can determine the four days of their births from clues 5, 7, and 8.
3. You can determine the four months in which they were born from clues 2, 6, and 10.
4. You can determine the years in which they were born from clues 4, 9, and 11.
Once you have determined this information, you can set up a table and solve.

Here is a table which I used to eliminate the other possibilities:

Name   1st
(oldest) 		2nd 3rd 4th   Jan Feb Mar Apr May Jun   2 18 28 29   1998 2000 2004
Kate   X X O X   X X X X O X   X X O X   X X O
Jackson   X X X O   X X X X X O   X X X O   X X O
James   O X X X   X X O X X X   O X X X   O X X
Carrie   X O X X   X X X O X X   X O X X   X O X

Correctly solved by:

1. Julie W. Dallas, Texas
2. Trey Mason Winchester, Virginia
3. Richard K. Johnson La Jolla, California
4. Jeffrey Gaither Winchester, Virginia
5. Elizabeth Cotter Ponte Vedra Beach, Florida
6. Nicholas Hung Toronto, Ontario, Canada
7. Tyler Windham Columbus, Georgia
8. Crystal Church Columbus, Georgia
9. Walt Arrison Philadelphia, Pennsylvania
10. Dave Smith Toledo, Ohio
11. Jason LaRusso Winchester, Virginia
12. Misty Carlisle Winchester, Virginia
13. David & Judy Dixon Bennettsville, South Carolina
14. Arin Smith Winchester, Virginia
15. Rich Murray Ridgetown, Ontario, Canada
16. Chris McCormick Virginia Tech,
Blacksburg, Virginia
17. Martin Dominguez Olympia, Washington
18. Dashiell Quasebarth Winchester, Virginia
19. Emily Auerbach Columbus, Georgia
20. Sarah Jane Wright Columbus, Georgia
21. Viktor Logrell Tullängen, Örebro, Sweden
22. Jonas Sutinen Tullängsskolan, Örebro, Sweden
23. Joakim Berggren Tullängsskolan, Örebro, Sweden
24. Erik Ekman Tullängsskolan, Örebro, Sweden
25. Lisa Sevón Tullängskolan, Örebro, Sweden
26. Jackie Henson Columbus, Georgia
27. Alex McIntire Columbus, Georgia
28. Cameron S. Columbus, Georgia
29. Sally Pound Columbus, Georgia
30. Gustav Nilsson Tullängskolan, Örebro, Sweden
31. Sanna Lejegren Tullängskolan, Örebro, Sweden
32. Josh Feingold Cailfornia Institute of Technology,
Pasadena, California
33. William Chyr Toronto, Ontario, Canada
34. Shannon Bagshaw University of Virgionia,
Charlottesville, Virginia
35. Bahadir Güngör Tullängskolan, Örebro, Sweden
36. Erik Hultgren Tullängskolan, Örebro, Sweden
37. Daniel Kvist Tullängskolan, Örebro, Sweden
38. Joanna Sturk Tullängsskolan, Örebro, Sweden
39. Linda Axelsson Tullängsskolan, Örebro, Sweden
40. Randa Tams ----------
41. Jonathan Jansson Tullängen, Örebro, Sweden
42. John Harcourt Columbus, Georgia
43. Kris Hon Toronto, Ontario, Canada
44. Victor Lee Toronto, Ontario, Canada