Thursday, December 16, 2010

The Perfect Presents Puzzle

Image by triplezero, distributed under CCL.

You are going to visit your friend in Chicago for the winter Holidays and emailing her to find out the exact ages of each of her 3 children (all girls) to buy them presents. She is texting you back, but apparently distracted with the fever of her youngest daughter, all she writes is that she wants to talk to you about kindergarten for the next year. She also mentions that last night kids calculated that the product of their ages is equal to her age. You search on Facebook and see that she was born in May 1974. What are you to do about the presents? Is there any way to figure out her kids' ages?

Answers accepted all day long on Friday, on our Family Puzzle Marathon. They will be hidden until Saturday morning (EST) and everyone who solved correctly will get a puzzle point.


Tom said...

Mom is 36 right now. 6,3,2. Nobody can be 5.

3,3,4 would multiply correctly but the kindergarten next year makes that less likely.

If the children's math is correct, that is.

Kim said...


* born in 1974, the mother is 36
* she has three children
* the product of the ages of the children is her age (36)

36 prime factors to 3x3x2x2, so the ages need to be combinations of these. Possible ages are 18,9,6,4,3,2,1

We know one of the kids is going to be in kindergarten next year, which probably makes her 4 now. That immediately wipes out the 18 as a possibility.

Now you have two kids left whose ages have to multiply to 9. They could be 9 and 1 or 3 and 3.

If the hint about the "youngest daughter" is meant to imply that there are not youngest twins, then the ages 9,4 and 1.

Otherwise, they could be 4, 3 and 3. (Of course, you might also argue that the hint about the kids doing the math implies that this possibility is highly unlikely and 9, 4 and 1 clearly is the best answer).

Her Grace said...

The girls are 2, 3, and 6.

Kate Arms-Roberts

Her Grace said...

She is 36. So, ABC=36.

The girls are 2, 3, and 6. Unless she has twins, in which case, the girls are 1, 6, and 6.

Kate Arms-Roberts
answer #2 [corrected for completeness from first answer]

anne-marie said...

I think that if she wants to talk about kindergarten, she probably has a four years old girl going to five.
Now, she said kids and not her kids calculated that the product of their age is equal to her age. She is 36 yo. She probably has a 9 years old able to do multiplication.
My answer is: 1 year old, 9 and 4.

Maria said...

For all those not familiar with the US school system, who doesn't have kids or had them long time ago. Kids start kindergarten in US nowadays when they are 5 years old.

SteveGoodman18 said...

The children's ages are 9, 4, and 1.

We will assume that all ages are integers only. The mother's age is 36. Since a child is beginning kindergarten next year (and we will assume this is not a child who will start kindergarten early), one of the children is either 4 or just turned 5. However, 5 is not a factor of 36, so there mus be a 4-year-old.

This leave the other two children with their ages having a product of 9. This can be done in two ways - 3-year-old twins, or a 9-year-old and a 1-year-old. Since a reference is made to the "youngest" child having a fever, we may assume that there is just one youngest child, and therefore no 3-year-old twins.

This leaves the only possibility of having a 9-year-old and a 1-year-old to go along with the 4-year-old.

kj said...

I calculate their ages as 9, 4 & 1.

My first assumption is that the children used whole numbers for their ages when multiplying them together.

My second assumption is that everything is straightforward about this -- i.e. the friend doesn't have a precocious three-year old who will turn four in the not-too-distant future, who she thinks should start kindergarten early at age four and a half next fall.

The friend is currently 36 years old, as her last birthday was in May and she was born in 1974.

That means the possible ages for her children are:
12, 3, 1
9, 4, 1
9, 2, 2
6, 6, 1
6, 3, 2
4, 3, 3

I conclude at least one daughter will enter kindergarten next year, and so either turned five this fall, or will turn five before next fall (or whenever the cutoff date is for her town -- for some towns it is September 1, others October 1, others December 1).

This means the children are either 9, 4, & 1 or 4, 3, & 3.

Since the friend was concerned about her youngest daughter's fever, she does not have three year old twins. Also, the fact that the children could do multiplication, makes me think that one is already school-age (and many schools don't teach multiplication until third grade, and third graders usually are eight or nine years old).

Therefore, the children are 9, 4, & 1.

Heidi said...

You can solve this, but you have to make some assumptions:
- that the mother has already had her birthday this year, making her age 36
- that the child entering Kinder next year has not already turned 5, making her age 4

There are 2 possible answers with a product of 4 that multiply to 36:

4x3x3=36 and

Because the friend mentioned that her "youngest child" (not children) had a fever, you can assume she doesn't have 3 year old twins.

Therefore, she has a 9, 4 and 1 year old. Now the real puzzle becomes what to buy the 9 year old that won't cause her to roll her eyes and turn up her nose. That would truly be a Christmas miracle!

Donna said...

The friend's age is 36. (2010 - 1974) The daughter who will be starting kindergarten next year would be 4 years old right now. Since the product of the 3 girls' ages is 36, that means if I multiply all 3 ages together I get 36. So the product of the remaining two daughters' ages must be 9, since 4x9=36. So either the friend has twins, each 3 years old, or one girl is 1 and one is 9. Since you specified "youngest daughter", I am assuming different ages for all the girls are 1, 4, and 9 years old.

Hari Atma Kaur Khalsa said...

Well kids starting kindergarten can be 5 or sometimes 6yrs old. I came up with 4yrs for one child because she was talking about planning for next years kindergarten. So one child is 4yrs old and she has a set of twins that are 16yrs old.

Fe said...

Thank you for the "disclaimer" about kindergarten age in the US. I was going to say, "it depends on what age kids start kindergarten".
Well, that would make my final answer: 1, 4, and 9.
Mom is 36 years old. The soon-to-be kindergartener next year is 4 years old. The oldest is 9. And the youngest with fever is 1.

Wang said...

The friend in Chicago was born in 1974 so she is 36 years old.

Since she has 3 kids that multiply to 36, we can figure out the different factors of 36.




We have a few pieces of information to determine the ages of her children. First, she mentions that she has to deal with the fever of her youngest daughter (therefore, the ages of the children can't be 1,1,36 or 2,2,9 or 3,3,4 since she would then have two youngest daughters)

Secondly, thanks to Maria, we have the kindergarten piece of information. Since she is talking about Kindergarten for next year, one of the kids must be 4.

With these two pieces of information, only one combination works : 1,4,9

Therefore, her kids are aged 1, 4 and 9.

Pat said...

If her child hasn't started kindergarten yet,the child is probably 4 years currently. If the mother was was born in 1974, she is 36 years old. If one child is four years old because it starts kindergarten next year, then the product of the other two is nine. Possibly the other two are three year old twins or Irish twins (less than a year apart). Another possiblityis that two of the girls are 4 years old,and the other is 27 months.
I would like to know how just how many 4-year-olds know how to multiply?

Kim said...

Just realized I left out the possibility that the kids are 6, 6 and 1 - but the 6 year olds would be too old for kindergarten next year. So back to my original answer of 9, 4 and 1.

Maria said...

Our friend in Chicago has three daughters that are: 1, 4 and 9 years old! We hope her youngest baby feels better today and we need to remember to talk to her about kindergarten for her 4-year old that will start kindergarten next September.

The friend is 36 years old as you figured out from the Facebook and her kids ages should multiply to 36.

Yes, she can't have 3 year old twins and 4 year old because they can't multiply yet and she wouldn't be referring to one of the 3 year old as a youngest daughter.

You all are amazing! Sorry to those who didn't know at what age kids start kindergarten here in US. I tried to add this information in the comment midday Friday. Puzzle points to Kim, anne-marie, SteveGoodman18, kj, Heidi, Donna, Fe, Wang for the correct answer.

A tricky Holiday puzzle next Friday!

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