The Toyota Camry Good Will Hunting Hidden Math Challenge

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There is a new Toyota Camry commercial out right now, and there is a secret math problem hidden inside of it.  The ad features the Boller family whose parents have been continually passing down a Camry to their progressively younger children.  I’ve been glued to the TV for the past month waiting for the commercial to re-air and seeing If I could gather enough information to figure out the exact age of all the children.  I kept thinking that if I solved the math problem I would somehow get a free Camry.  Or something.  I don’t know.  But, after finding the commercial on YouTube and watching it repeatedly, I have been able to isolate all the pertinent information.

1.) The Boller family bought a new 1997 Camry.  I can’t be positive, but I think we’re supposed to assume that means it was, in fact, purchased in 1997.

2.) When the older daughter turned 16, she got the Camry

3.) The older daughter drove the Camry for 9 years until…

4.) The younger daughter turned 16, and then she got the Camry and was like, “Yessssssss!”

5.) The son hopes that in the future he will get the new 2010 Camry Hybrid the Boller parents just bought.

Check it out:

Unfortunately, this is not enough information to precisely nail down all of their ages.  But here’s what we can figure out from the data.  The absolute oldest that the older daughter could possibly be right now is 29.  That, however, is presupposing that she turned 16 in 1997, the same year her parents got their first Camry.  Though that specific scenario is highly unlikely, we can’t rule it out entirely.  So that’s where we’re stuck with her upper age limit — the older daughter is no more than 29 years of age.

We also know that the older daughter drove the car for 9 years and then gave it to her sister who had by then reached the age of 16.  That means there is a 9 year age difference between the two. That puts the younger sister at no more than 20 years of age at the current moment.  And given that 9 year age difference and knowing that the younger daughter is currently driving the car, we can also surmise for both daughters a lower age limit.  The most recently the younger daughter could have received the Camry would be this year which would make her youngest possible current age 16 and the older sister’s youngest possible current age 25.

When it comes to the son, we have too few necessary figures.  He is a mystery.  All we know for sure is that he is below the legal driving age, probably by a couple of years.  So, to review:

25 < Older Daughter < 29

16< Younger Daughter <20

Son significantly < 16.

BUT WAIT!  THERE’S A HIDDEN PASSAGE WAY TO MORE CLUES!!

You might not have noticed, but on the YouTube version of the commercial, this happens at the 00:31 mark:

“Want to see the Bollers’ whole story?”  You’re goddamn right I do.

When you click on that link, it leads you to another video that has a treasure trove of math hints and songs about it being “time to get uuuuuuuuuuuuup!”

First of all, awesome family, guys.  I don’t know how to not sound sarcastic here, but the Bollers actually seem like a ton of fun.  But that’s not what this is about.  This is about the math.

We find out from this video that, though the Camry is a 1997 model, it was actually bought in 1996.  Not cool, Toyota.   That is critical information I could have used in the for-TV commercial.   Now we have to adjust all of our original numbers to account for your negligent omission.

25 < Older Daughter < 30

16 < Younger Daughter < 21

Son = still some indeterminate age < 16

Anyway, we learn that in 1996, the younger daughter was 3.  And we can assume it was late 1996 because the next year’s car models were already out, so that puts her currently at 17 or, at the very least, on the last few months of her 16th year.  I guess she pretty recently got the Camry.  Congratulations, younger sister! And the older sister is 9 years her senior so that makes her 26.  Then BOOM!  Right at the end, the mom just tells us the son is 14.  We did it, you guys.

Older Daughter :     26

Younger Daughter: 17

Son:                        14

The math problem is solved.  We all deserve a free Camry.

ME: Beethoven, okay. He looked at a piano, and it just made sense to him. He could just play.
YOU: So what are you saying? You play the piano?
ME: No, not a lick. I mean, I look at a piano, I see a bunch of keys, three pedals, and a box of wood. But Beethoven, Mozart, they saw it, they could just play. I couldn’t paint you a picture, I probably can’t hit the ball out of Fenway, and I can’t play the piano.
YOU: But you can solve a Toyota Camry commercial in under an hour.
ME: Right. Well, I mean when it came to stuff like that… I could always just play.

If anyone noticed any math errors, please feel free to correct me.  Also, you get so many bonus points if you can somehow pin down the parents’ ages.

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