The greatest treasure my grandfather left us was his letters, capturing his thoughts, interests, passions, opinions, insights, and grandfatherly wisdom gained over his lifetime. They also included many, many math and logic puzzles which he had collected or made up and delighted in sharing.
From the time I was in eighth grade through my college years, Papa, as all the grandchildren referred to him, wrote weekly letters that he then photocopied at a local library and sent individually to his two daughters and all the members of his extended family. I saved most of his letters in cardboard shoeboxes, but inevitably many were lost. Fortunately, my mother and Aunt have since recovered, organized, and retyped all the handwritten letters, and with the help of my jack-of-all-trades cousin, they will soon self-publish these letters as a 350-page book for family members here and abroad. The letters capture the essence of a remarkable man, and the book will surely be passed down to my children, and someday from them to theirs.
Papa came from a respected Orthodox family in London. His father, born in Mogilev in Eastern Belarus,was a Torah scholar who served as the Rosh Hashochetim (head trainer, inspector, and Kabbala [license] provider for kosher meat production) for all of England and Ireland. Rav Kook, then chief rabbi in Palestine and one of the great Torah scholars of his time, wrote a glowing endorsement of my great-grandfather which might have helped him secure his position.
Papa left England as a young man, worked at a Hebrew Orphanage, taught math at Temple University, and later became an actuary. If you own a variable annuity or universal life insurance policy, then you have my grandfather to thank (or blame), because he pioneered the development of both. In his obituary, the Council of Actuaries credited him with developing the concept of a flexible life insurance plan that was eventually marketed as universal life. Additionally, he published the first actuarial paper on the variable annuity. Above all, Papa was a philosopher, a man who loved to share his mastery of logic and reasoning through clever puzzles and thought-provoking essays.
In another column, I will share snippets of Papa’s thoughts about a range of ethical and philosophical issues. For now, here are six of his countless math and logic puzzles which he shared with his extended family for them to ponder in their spare time. Papa invented some of these puzzles, and found others in puzzle books. Incidentally, most of them can be solved with basic arithmetic skills, which doesn't mean that all of them are easy (at least not for me).
If you enjoy puzzles I invite you to try to solve at least one of them! If you want to post an answer or explanation, please refer to the puzzle by number.
Puzzle 1 – HOW LONG IS THE SHELF
A shelf is exactly filled with books of equal thickness.
If the books were 1” thinner, the shelf would accommodate 6 more books.
If the books were 1” thicker, then there would be no room for 3 books.
How many inches long is the shelf?
Puzzle 2 – HOW OLD ARE BERT'S CHILDREN?
Bill is the Insurance Agent. Bert is the prospect for Insurance.
Bill: So you are just 40 – with three kids. How old are they?
Bert: Figure it out for yourself. The three ages add up to the street
number of this house. If you multiply their ages together, the
result will be my age.
Bill: I still can’t tell their ages.
Bert: Forget it then. The two elder kids will be walking back from
school now; so you will meet them.
Bill: That’s all I need to know.
Bill then gave the three ages without delay.
What are the three ages?
Puzzle 3: HANGED OR DROWNED?
A man has committed a crime punishable by death.
He is to make a statement.
If the statement is true, he is to be drowned.
If the statement is false, he is to be hanged.
What statement did he make to confound his executioners?
Puzzle 4: STRAIGHTFORWARD MATH?
What number leaves a remainder of 1 when divided by 2, 3, 4, 5, 6, 7, 8 and 9, respectively, but leaves no remainder when divided by 11?
Puzzle 5: MEASURING THE BOOKWORM
On January 1, I started to read a book and by reading the same number of pages each day of the month, I managed to finish it on the 31st of January (include the 31st).
If I had started by reading a quarter of that number of pages on January 1, and on each succeeding day, one page more than on the preceding day, I should also have finished it on January 31 (include the 31st).
How many pages did the book contain?
Puzzle 6: WHO DONE IT?
Four men were eating dinner in a restaurant when one of them suddenly struggled to his feet, cried out: “I’VE BEEN POISONED” and fell dead.
His companions were arrested on the spot and under questioning made the following statements, exactly one of which is false in each case.
WATTS: I didn’t do it
I was sitting next to O’NEIL.
We had our usual WAITER today.
ROGERS: I was sitting across the table from SMITH.
We had a new WAITER today.
The WAITER didn’t do it.
O’NEIL: ROGERS didn’t do it.
It was the WAITER who poisoned SMITH.
WATTS lied when he said we had our usual WAITER today.
Assuming that only SMITH’s companions and the WAITER are implicated, WHO WAS THE MURDERER?