[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 ;)