[intrasight]

When my daughter was 10 we were waiting in line to checkout at a Home Depot. She asked me what was algebra. I think she had heard the older kids mention it. I responded with a question. "A plus B = 10, and A minus B = 1. What are the values of A and B?" She puzzled it over while I check out. Then her face lit up like a whole realm of knowledge had just opened up to her, and she proudly told me the answer. It's a special moment that we will both always remember. She told me that as a camp counselor that she has challenged younger kids who seemed bored with the same problem.

Do challenge your kids intellectually beyond their years and you might be pleasantly surprised. My daughter heads to CERN in two weeks to study anti-matter, and I have no doubt that our brief intro to algebra at a Home Depot has a small role to play in that journey. Maybe Star Trek did too :)

[bjoli]

As someone who takes pride in having solved the first 100 problems of project Euler, I am slightly ashamed to admit that I probably spent as much time as your daughter to solve that.

I got stuck thinking in integers, and quite quickly left the exercise as an oversight in writing the post (since X + y = even, X - y = odd is impossible for integers)

3 seconds into the first coffee of the day the realisation of my stupidity hit me in the face.

[mixmastamyk]

It's impossible until it's easy, like any good trick question.

[bpizzi]

For the posterity: {a+b=10;a-b=1} translates to {a+b=10;a=b +1}, thus the first equation is ((b+1)+b=10) giving (b=4.5), and from there we get (a=5.5).

[LolWolf]

Another fun way: add the two equations to get 2A=11 and subtract to get 2B=9.

[LolWolf]

I mean, is there any other solution? There are certainly no integral solutions to the problem, but there is a unique (rational) solution.

I feel like I’m missing something entirely, though...

[Sharlin]

I was also stuck thinking in integers for a few seconds, perhaps because of the context. But yeah, a 10-year-old would already know about fractions.

[endeavour]

I also mentally started thinking about integral solutions. I wonder if it's also because of the variable names... a,b,c tend to be used to represent integers (e.g. Fermat's Last Theorem, Euclid's algorithm etc).

x and y are more commmonly used to represent real numbers.

[dzdt]

Random aside: once in high school I took a math puzzle test. The only problem I skipped was because they asked for "integral solutions." I knew the word "integral" only as belonging to calculus, about which I knew nearly nothing at the time. If I had realized in context it just meant "integer" I could have done it!

[intrasight]

They did make it a tricky question!

[intrasight]

Thanks for pointing that out. I'll use X and Y next time I share this story. Of course my daughter wouldn't have known at the time about the distinction, and neither did I - it having been too long since doing algebra ;)

[icc97]

Coincidentally a friend at University had a dad who worked at CERN. His number one goal was to not work at CERN.

[intrasight]

Do you know why?

[inanutshellus]

(My guess)

She spent her teens trying to get away from dad, why spend her working life there? :)

[icc97]

I'm not totally sure why. The life living on the boarder between France and Switzerland seems pretty idyllic (but at the end of university you don't think about that so much). I got the feeling it was just that going to work where your dad is isn't very appealing no matter where it is.