Mr. P taught mathematics and computer science for over 40 years at the following schools:
Dolgeville Central School (Dolgeville, NY),
Hartwick College (Oneonta, NY),
Washington-Lee High School (Arlington, VA),
Herndon High School (Fairfax, VA),
John Handley High School (Winchester, VA),
James Madison University (Harrisonburg, VA), and
Lord Fairfax Community College (Middletown, VA).
Mr. P has been happily married since 1968 and has three adult children and seven grandchildren.
Mr. P is now retired and living in Colorado.
Mr. P enjoys the music of Simon & Garfunkel, Elvis, Boney M, Alison Krauss, Buddy Holly, The Eagles,
Jimmy Buffett, Queen, The Nitty Gritty Dirt Band, Meat Loaf, Alabama, among others.
To find out more about him, you must solve the following puzzles
which he created at various times in his life:
In 1987, I made the following statements:
- I lived 1/8 of my life before going to school.
- Then I went to school for 2/5 of my life.
- Immediately after graduation, I married my wife Carol.
- Then I taught at Herndon High School in Fairfax County for 1/8 of my life.
- I have spent the rest of my life teaching at John Handley High School in Winchester, VA.
- I have been married for 19 years.
- After 3/5 of my life, my daughter Amy was born.
- After 3/4 of my life, my daughter Sarah was born.
- My son Michael was born 2/3 of the way between my two daughters' births.
- How old was I? _________
- How old was I when I got married? ________________
- How old was I when Amy was born? ___________________
- How old was I when Michael was born? _______________
- How old was I when Sarah was born? _______________
Mr. P made the following statements about his grandchildren in 2004:
- Mr. Pleacher has four grandchildren.
- 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.
- 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.
- Three of the grandchildren were born in Leap Years, but the oldest was not.
- Carrie's birthday was on the 18th of the month, and the oldest was born on the 2nd of the month
- None of the grandchildren was born in January or July.
- The sum of the days on which they were born is 77.
- The youngest was born on the 29th of a month which has 30 days.
- James was born in 1998.
- Kate was born in May
- 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?
Then I made the following statements about my life on New Year's Day, 2007:
- I spent five years at home before starting school.
- Then I spent 4/15 of my life in school.
- After graduating from college, I immediately married and began teaching.
- My son, Michael, was born 2/3 of the number of years between my older daughter's birth (Elizabeth) and my younger daughter's birth (Sarah).
- Ten percent of my life passed between my two daughters' births.
- I lived 1/2 of my life from the time I was married until my grandson James was born.
- Elizabeth was born after I had lived 2/5 of my life.
- My granddaughter Carrie was born 1/3 of the way between the year that James was born and the year that grandchildren Kate and Jackson were born.
- I retired one year after James was born and one year before Carrie was born.
- Seven twentieths (7/20) of my life passed between the year Sarah was born and the year that James was born.
- My grandson Ben was born two years after Jackson and Kate were born.
Can you answer the following questions?
- How old is Mr. P now? _____
- How old was he when he was married? _____
- How old was he when Elizabeth was born? _____
- How old was he when Sarah was born? _____
- How old was he when Michael was born? _____
- How old was he when James was born? _____
- How old was he when Carrie was born? _____
- How old was he when Jackson was born? _____
- How old was he when Kate was born? _____
- How old was he when Ben was born? _____
- How old was he when he retired? _____
In September 2010, Mr. P made the following statements about his life:
- I graduated from college and started my teaching career after I had lived 1/3 of my life.
- My daughter Sarah was born after I had lived another 1/7 of my life.
- Two years before she was born, my son Michael was born.
- My daughter Amy was born four years before Michael was born.
- Another 1/3 of my life passed between the birth of Sarah and the birth of my first grandson James.
- Then another two years passed before granddaughter Carrie was born.
- Four years after that, grandchildren Katie and Jackson were born.
- Then in two more years, grandson Ben was born.
- Four years after that, in 2010, grandson Stewart was born.
Can you answer the following questions?
- How old is Mr. P? _____
- How old is Amy? _____
- How old is Michael? _____
- How old is Sarah? _____
- How old is James? _____
- How old is Carrie? _____
- How old is Katie? _____
- How old is Jackson? _____
- How old is Ben? _____
- How old is Stewart? _____
On his birthday in 2011, Mr. P made the following observation:
For the first time in my life, both of the following statements are true:
(1) My age is the product of two different prime numbers; and
(2) Next year my age will be the product of three different prime numbers.
How old was Mr. P?
On September 1, 2015, Mr. P made the following statements about his seven grandchildren.
(1) Their names are Ben, Carrie, Elizabeth, Jackson, James, Katey, and Stewart.
(2) They were born in the cities of Albuquerque, NM; Bangor, ME; Fort Collins, CO; Greenville, SC;
Jacksonville, FL; and Reston, VA.
(3) They were born in the months of February, March, April, May, June, and July.
(4) Their ages are 17, 15, 11, 9, 5, and 0.
(5) Two of them were born in the same month; two of them were born in the same city; and two
of them are the same age but one month apart.
(6) The sum of their ages is the same number as Mr. P's age, and Mr. P was born in December of 1946
(don't bring presents - just send money).
(7) Mr. P's granddaughters were all born in April and May.
(8) The 9-year old is Jackson's brother and they were born in the same city.
(9) The person born in March was not born in Fort Collins or Albuquerque.
(10) The two people with the same age were born in consecutive months.
(11) Jackson and the grandson born in March were not born in Jacksonville.
(12) The grandchild born in Reston is older than the grandchild born in Jacksonville.
(13) The 15-year old and the grandchild born in Bangor were born in the same month.
(14) Ben's birth month comes after his brother's.
(15) Stewart is younger than Katey but older than Elizabeth.
(16) The youngest was born in Bangor and the oldest was born in Greenville.
(17) Ben, Jackson and the 5-year old were born west of the Mississippi River.
(18) James is 8 years older than Ben
(19) Carrie's age is three times the age of the person born in Albuquerque.
Can you determine the age, the birth city, and the birth month for each of Mr. P's grandchildren from the nineteen clues above?
The inspiration for some of the problems above came from the epitaph on Diophantus' Tombstone.
Click here to see the epitaph on his tombstone
In November 2012, Mr. P made the following statement:
I will turn x + 34 years old in the year x2.
How old will Mr. P be on his birthday this year?
The inspiration for this problem came from a quote by Augustus De Morgan when asked about his age.
He said, "I was x years old in the year x2."
Augustus De Morgan (27 June 1806 - 18 March 1871) was a British mathematician and logician who developed DeMorgan's Laws.
Since he was born in 1806, he was 43 years old in 1869 (which is 432).
In December 2017, Mr. P posed the following problem:
Can you determine the ages of Mr. P's Grandchildren from the 7 clues below?
Give the age for each of the following grandchildren: