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Tammy's Age

Math brain teasers require computations to solve.


Puzzle ID:#7963
Fun:*** (2.48)
Difficulty:*** (2.99)
Submitted By:snaps*au*****
Corrected By:MarcM1098




I was talking to a friend Tammy, the middle child of five. She has a younger sister Tracey, and three brothers Tommy (oldest child), Timmy and Tony (youngest child). I asked her how old she was, but she hardly ever gives a straight answer. The following is the conversation we had.
"How old are you Tammy?"
"I am three times as old as Timmy was when Tony was born. Actually, it's funny, but Timmy's, Tracey's, Tommy's and my ages were all factors of Mum's age when Tony was born. The only other year where the ages of more than two of us were factors of Mum's age was when Tracey was half as old as I am now."
"How old is your Mum now?"
"There's another funny thing. When Mum turns 50, Tony will be the same age Mum was when she gave birth to Tommy."

Assuming Tammy was talking in terms of whole years, and with my mathematical and reasoning abilities I was able to quickly deduce not just Tammy's age, but all of their ages. So how old are Tommy, Timmy, Tammy, Tracey, Tony and Mum now?

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Oct 19, 2002

Wwwwoooowww, GR8, took me hours just to understand your answer.
Oct 19, 2002

Took me ages to understand the answer as well, and I wrote the thing!
Apr 11, 2003

Great Question, It took me about 40 minutes of guessing and checking to get the correct answer. I suppose it would be easier if I had learned the right algebra, but I'll do that in year 11 or 12 probably.
Mar 06, 2005

Fun, enjoyable teaser.
Apr 21, 2005

Loved it! I had a lot of fun with it for a couple hours, and if felt great when the answer suddenly appeared! Phew! Thanks!!!
Jan 11, 2009

Wow. One of the hardest yet. Awesome teaser!
Jun 04, 2012

Great teaser. Quite hard. I first deduced that I had to find 4 discrete factors of a number < 50. Turns out all combinations begin with either 1 x 2 x 3 or 1 x 2 x 4.
The first set leads to Tammy being 9 but Tammy must be an even age (reference to half her age). Therefore It must be 1 x 2 x 4 and Tammy is 12. Thus the Youngest children are 10, 11, 12 and 14. five years ago they were 5, 6, 7,9. Any combination of 3 factors is too large unless they overlap so 6 and 9 must be two of the factors. So eldest was a multiple of 6 and 9 i.e. 18 five years ago. Now we have the answers.
Excellent teaser.

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