Answer to the September 27, 2004 Problem of the Week

The Grandchildren Problem

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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?

 

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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: