Ken's blog

Two grandfathers sat discussing their families on a bench under an olive tree.

“How old is your granddaughter Rachel, Moishe?” asked Benny.

“Well, I’m twelve times older than Rachel.”

“How about some more info, Moishe.”

“Well, her mother, Sarah, is six times older. And her mother’s age divided by two gives a remainder of one.”

“Any other details you can offer?”

“Sarah’s age divided by three, four and eight also give a remainder of one, but five none,” added Moishe.

“Thanks, Moishe, that’ll do the trick.”

“And how old is your granddaughter, Miriam, Benny?”

“Twice Rachel’s age plus eight months.”

The two grandfathers continued discussing their families on the bench under the olive tree.

Can you work out the ages of Moishe, Sarah, Rachel and Miriam.

“How old are you and your wife, Capt. Haddock?” asked the insurance man.

“When we were married 18 years ago I was thrice as old as Julia. Now I am twice her age,” said Capt. Haddock.

“Hmm…“ The insurance man was busy scribbling in his notebook.

Can you work out the present ages of Capt. Haddock and his wife?

¨How many brothers do you have, Benny?” asked Jasper.

“I have just as many brothers as sisters,” said Benny.

“How many siblings do you have, Joan?” asked Jasper of Benny’s sister.

“I have twice as many brothers as sisters,” said Joan.

Can you work out how many siblings there were in Benny’s family?

On an snowy Sunday afternoon, Friedrich was walking down an icy street deep in thought when he bumped into his mathematician colleague Leonard.

“Hi Leonard, nice to see you again,” mumbled Friedrich absent-mindedly, his breath emanating from his nostrils as fog in the cold.

“Likewise, Friedrich. You seem to be absorbed in something,” observed Leonard while smacking his gloved hands together to keep warm.

“Yes, you are right. I just came from visiting my brother Pascal and his family. He gave me a conundrum for the ages of the children of his brother-in-law, which I am ruminating on,” said Friedrich, scratching his head.

“I’m completely curious,” said Leonard with big eyes.

“Ok, Leonard, here you have the convoluted puzzle. Let’s see what you can do with it,” said Friedrich:

“When Albert is a third as old as Tina will be the year before when Albert is half as old as Lola is now, Tina will be twice as old as Lola was when Albert was half his current age.”

“A year ago Tina was older than Albert’s current age by one eighth of the product of Tina and Lola’s present age difference and that of Lola and Albert.”

“What do you think about it?” inquired Friedrich.

“Well, it certainly is something to chew on. I suggest we head for a fine warm French bistro I know about just around the corner,” invited Leonard.

“Ok, last to solve the puzzle pays,” smiled Friedrich.

Can you help Friedrich and Leonard work out the ages of Albert, Tina and Lola?

Fred, a mathematician, was walking leisurely down a sunny street on a Saturday afternoon when he spotted his colleague Leonard that he had run into not so long ago.

“Hello Leonard, nice to see you again.

“Likewise, Fred, I see you are well,” replied Leonard, shaking his hand.

“Last time we met we spoke about my children, Fred. Do you have any children?“ queried Leonard.

“Yes, I do, I also have three children. I married your old girlfriend Jo Anne after you left for university,” said Fred.

“Really Fred, glad you two hit it off,” replied Leonard. “I wonder how old your children are.”

“As you are a colleague, I will give you the answer in a mental package as you gave me before,” smiled Fred.

“Ok, shoot,” said Leonard.

“The sum of the square of the ages of Bill and Mary add up to the sum of twice the product of Mary’s and Leo’s ages plus thrice Leo’s age. When Bill is twice as old as he is now he will be one year younger than Mary at that time and one year older than Leo at that time,” informed Fred with a magnanimous grin.

“Hmm, Fred, a bit muddy, could you give me some more information,” said Leonard.

“The sum of their ages when Bill is twice as old as he is now will be 36,” offered Fred.

“Well, that’s better,” replied Leonard, thought a moment and offered Fred the correct ages of his children.

“Let’s head over to a fine café I know of down the street for a nice chat,” said Leonard.

What do you say are the ages of Fred’s children?

A mathematician walking leisurely down a street on a Sunday afternoon spotted a colleague he had not seen for some time.

“Hello Fred, nice to see you.

“Likewise, Leonard, I see you are well,” replied Fred, shaking his hand. “Did you ever marry Helen?”

“Yes, I did and now we have three children,” replied Leonard.

“Glad to hear it. How old are your children,” asked Fred.

“As you are a colleague, I will give you the answer in a mental package,” smiled Leonard.

“Ok, hand it over,” said Fred.

“Well, the sum of their ages is a perfect number. Twenty-one times Sarah’s age is the ninth heptagonal number. The product of their ages is a number whose double cross sum is nine. Jason is five years younger than Alex. Is that sufficient information for you,” chuckled Leonard.

“More than sufficient,” replied Fred and promptly gave Leonard their correct ages.

“Next time I see you, I will also set you a small task,” laughed Fred and invited Leonard to come along to his favorite inn to discuss old times.

“Can you tell me about the ages of the new caretakers, the Jones family?” asked the math student Lanoo of his teacher Orion.

“Yes, I will be happy to. Perhaps you won’t be so pleased,” smiled Orion, “when smoke starts coming out of your ears.”

“The difference between the ages of John and Mary is twice that of Cuthbert.

One of the former is ten times as old as Cuthbert. Reading backwards, the age of John is the same as that of Mary.

What are their ages?”

A mathematician named Albert meets a colleague and says: “Nice to see you again John. How is life?”

“I am prosperous, Albert, and happily married with three kids.”

“That’s nice. How old are they?” asked Albert.

“The product of their ages is 36 and the sum is equal to the number of swans you can see in my private lake,” pointing out the window.

Albert thought for a while, then he said. “That’s not enough information, John”

“You are right, I forgot to tell you that the age sum divides that of their squares,” replied John.

Albert thought for a while, smiled and said: “Ok, now I know how old they are, John”

How old are the kids and how many swans are in the private lake?