I met the dad of a homeschool family on the plane yesterday who told me a riddle. Now that I’ve enjoyed solving it, I thought I would share it with you:

Two math moms, Lisa and Gwen, are carpooling to a play date with Heather. Lisa is telling Gwen about Heather and her family. The conversation turns to the ages of Heather’s three children.

Lisa says, “If you multiply their ages together, you get 36.”

Gwen says, “How nice, but that doesn’t give me enough information to determine their ages.”

“Good point. If you add up all of their ages, you get that house number,” Lisa says pointing to a house.

“Interesting,” Gwen says, “but that’s still not quite enough information.”

Lisa says, “Well, you’ll meet two of them soon. But the oldest is with her grandma.”

“Oh, great,” Gwen says, “They’re perfect ages to play with our kids!”

### What are the ages of Heather’s kids?

The end of the riddle is “what are their ages?” But the real value in the riddle is the logic and work it takes to arrive at the final answer.

The “answer” is easy, but getting there (or explaining how you got there) is much more challenging.

There’re not that many possibilities. So the trick is to imagine what each mom is thinking as they talk. What makes Gwen think, “that’s not enough information”?

### Share this with your children.

Tell this riddle to your children. Let them play with it. If they get discouraged and want a hint, ask them these questions – one at a time – and see how far they can get:

- What are all the possible answers? In other words, what sets of three numbers can multiply to give you 36?
- Lisa points to a house number. What are the possible numbers that are the house number?
- Go through each possible answer and imagine what Gwen was thinking when she said, “that’s not enough information?”

### And there’s more…

When your child solves the riddle, see if he or she can try to replicate it with other numbers. What kinds of things do you need to make another riddle just like this one, but with other numbers?

And don’t forget to share what happens in the comments below!

*(P.S. I’m specifically not giving the solution here because I believe it’s valuable to find the solution independently. If this angers you, tweet me and I’ll give you the answer.)*

###### You might also like:

- Math Problem Quickie: Prime Number Fun on Your Wedding Day
- Math Quote Cryptogram: Need More Space
- Math Quote Cryptogram: Trapped
- 7 Ways to Wrangle a Word Problem

Rich Text AreaToolbarBold (Ctrl + B)Italic (Ctrl + I)Strikethrough (Alt + Shift + D)Unordered list (Alt + Shift + U)Ordered list (Alt + Shift + O)Blockquote (Alt + Shift + Q)Align Left (Alt + Shift + L)Align Center (Alt + Shift + C)Align Right (Alt + Shift + R)Insert/edit link (Alt + Shift + A)Unlink (Alt + Shift + S)Insert More Tag (Alt + Shift + T)Toggle spellchecker (Alt + Shift + N)?

Show/Hide Kitchen Sink (Alt + Shift + Z)Easy Embed Tweet

FormatFormat?

UnderlineAlign Full (Alt + Shift + J)Select text color?

Paste as Plain TextPaste from WordRemove formattingInsert custom characterOutdentIndentUndo (Ctrl + Z)Redo (Ctrl + Y)Help (Alt + Shift + H)

I met the dad of a homeschool family on the plane yesterday who told me a riddle. Now that I’ve enjoyed solving it, I thought I would share it with you:

Two math moms, Lisa and Gwen, are carpooling to a play date with Heather. Lisa is telling Gwen about Heather and her family. The conversation turns to the ages of Heather’s three children.

Lisa says, “If you multiply their ages together, you get 36.”

Gwen says, “How nice, but that doesn’t give me enough information to determine their ages.”

“Good point. If you add up all of their ages, you get that house number,” Lisa says pointing to a house.

“Interesting,” Gwen says, “but that’s still not quite enough information.”

Lisa says, “Well, you’ll meet two of them soon. But the oldest is with her grandma.”

“Oh, great,” Gwen says, “They’re perfect ages to play with our kids!”

What are the ages of Heather’s kids?

The end of the riddle is “what are their ages?” But the real value in the riddle is the logic and work it takes to arrive at the final answer.

The “answer” is easy, but getting there (or explaining how you got there) is much more challenging.

There’re not that many possibilities. So the trick is to imagine what each mom is thinking as they talk. What makes Gwen think, “that’s not enough information”?

Share this with your children.

Tell this riddle to your children. Let them play with it. If they get discouraged and want a hint, ask them these questions – one at a time – and see how far they can get:

What are all the possible answers? In other words, what sets of three numbers can multiply to give you 36?

Lisa points to a house number. What are the possible numbers that are the house number?

Go through each possible answer and imagine what Gwen was thinking when she said, “that’s not enough information?”

And there’s more…

When your child solves the riddle, see if he or she can try to replicate it with other numbers. What kinds of things do you need to make another riddle just like this one, but with other numbers?

And don’t forget to share what happens in the comments below!

(P.S. I’m specifically not giving the solution here because I believe it’s valuable to find the solution independently. If this angers you, tweet me and I’ll give you the answer.)

thenor

You might also like:

Math Problem Quickie: Prime Number Fun on Your Wedding Day

Math Quote Cryptogram: Need More Space

Math Quote Cryptogram: Trapped

7 Ways to Wrangle a Word Problem

Path:

This post may contain affiliate links. When you use them, you support us so we can continue to provide free content!

I’m going to give this to my logical daughter who says she doesn’t like math but always is able to solve these kinds of questions.

Let us know how it turns out, Sandy!

I have to admit I haven’t really sat down to tackle this yet, but…I’m feeling a bit stupid that I don’t see how the last bit of information has any bearing on the numbers. How does where the children

aretell us anything about how old they are? Numerically, it doesn’t say anything except that they aren’t ALL the same age. But that wasn’t a possibility in the first place, was it?I think my daughter and I solved it. But if so, I think the riddle is imprecise. Will wait to see if hubby (the math wiz in our house) arrives at the same conclusion by the same reasoning.

Rachel Ramey recently posted..Personal Creations

Thanks for your comments, Rachel.

There’s IS a precise answer and the info IS important to that answer.

Enjoy!

I still think the riddle is imprecise. Even amongst twins, there is an older sibling.

Rachel Ramey recently posted..Our Favorite Yogurt

Good point, Rachel. Although I do think the intent was “older” means “a different integral number of years.”

But indeed, it is still a bit imprecise.