# Mathematical SBI contest #6 Results(2 SBI given away) and Solution of the Equation + Announcement

in #puzzle3 years ago

## Solution:

The problem of the last contest was:

For the first solution you need to factor out the x and y:
x*(x+1) = y*(y-1)
As you can see, on both sides there is a product of 2 consecutive integers. So the equation is true, when these integers are the same which is reached by y = x+1:
x*(x+1) = (x+1)*x
The next solution is a bit less obvious, and actually I even was surprised, when @tonimontana submitted it. Sadly that also means that I can't show you how to get to that solution. Maybe @tonimontana could do that in a comment?
I'll just show you that it works:
x²+x = y²–y | y = -x
x²+x = (-x)²–-x = x²+x

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

### How your chance of winning is calculated:

• Every participant gets 1 point for entering the contest.
• Every solution entered gets 1 additional point.
• Multiple examples of a general solution count as one solution
• If there is only one general solution, those who found its pattern(by mentioning a general formula or showing more then 3 examples) will get an additional point.
• Your winning chance is "your points"/"total points"

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

### List of participants with their scores and chance of winning, sorted by time of entry:

Namesolutions foundscorechance of winning
@contrabourdon(1, 2)220%
@sparkesy43(3, 4)220%
@tonimontana(x, -x), (x, x+1)330%
@onecent(x, x+1), (0, 0)330%

↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓↑↓

### Winner draw(using a self written program):

Congratulations @onecent, you won 1 SBI:

# Wait! Don't leave yet!

As I mentioned @tonimontana managed to surprise me with a solution I didn't think of. I thought similar to @onecent that 0 was a special solution, but @tonimontana proved this wrong. It won't happen often that I'm surprised, so I might as well reward you with 1 SBI:

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# Announcement

These contest cost some time and money to make. Finding equation of similar difficulty that are not based on the same principle is pretty hard, and liquid rewards from the posts are far less then 1 STEEM and I'm eating into my reserves.
I discovered that there seems to be more traffic around the weekend(not really surprising), so I decided to change posting times. Instead of creating a new contest every 3 days with an entry window of 2 days, I'll now make a new contest every 7 days(each friday) with an entry window of 5 days. That means the equations might be getting a bit harder, because you have more time, but that will also allow me to keep up the contest at a lower cost.

### The next contest starts tomorrow friday. Don't miss it!

Sort:
3 years ago (edited)

If you have one solution you can find the other by just looking at
x^2+x-a=0 where a:=y^2-y .
We already know x^2+x-a=0 has one real solution (x1=y-1). Factoring this polynomial gives x^2+x-a=(x-x1)*(x-x2) and comparing the coefficient of x we get 1=-x1-x2 or x2=-1-x1=-1-y+1=-y. This is how you could get x2.

I also send you some 1 Steem as a donation to support his contest because my upvote is worth absolutely nothing :)

Thank you, for both explanation and donation, although the last wasn't necessary, I still have 10.something liquid STEEM available, but I will use your donation to make a 2 SBI reward for the next contest.

Thanks for the SBI!

Way back when I was doing these - check out #brainsteem - I ended up mixing the questions so that some were fairly easy and could be done within a day, whereas others were trickier and were weekly.

As there are so many coders on steem, the computational mathematics questions became popular - similar to Project Euler (sometimes the same but with different numbers!)

Those are some interesting problems you posted back then. Why did you stop?

I'll soon try the unsolved one. I hope you still have the prize :P

Why did I stop? I got diverted by other projects, such as what became MAPR and the minnow community that preceded it.

The other issue was that we seem to have reached the saturation point of mathematicians on Steem! Or at least those who wanted to do puzzles. In my mind I wanted to create something like Stackexchange, but that is driven by a lot of students - students we really don't seem to have attracted here!

Now that there are more tools and platforms available, might be an idea to revisit that aim.

When I came to the platform I was really confused that there were challenges and contest for everything except math and science. One of the reasons I started making contests.

I think you should continue.

Well, now you know the last person to have tried!!

That's why I gave you some advice on tags. Any questions about how things worked, and didn't work, in the past feel free to ask.

Worthwhile project :-)

My favourite subject I teach is competition mathematics - I used to run a gifted kids club and was mainly maths, logic and random weird stuff.

I don't use my personal account much... maybe if we have 2 of us we may round up a posse! Students... we really don't have students on steem!!

I'll have to check - think I even had a maths trail.

Well there is one thing I'm especially interested about your past contests:
Where did you get your ideas?

maybe if we have 2 of us we may round up a posse!

What do you have in mind?

Students... we really don't have students on steem!!

That's wrong.
There is at least one student here on steem … and you are reading one of his comments right now.
Also I would guess there are a few more students hiding around here somewhere. We would just need to reach them somehow.
I thought rewards were a way, but you already tried that.
Maybe a high steem bounty would do, but that's too expensive and has a high risk of reaching nothing.
I'm at the moment using @contestkings to reach more people(That's where I used to search for useful contests.). Maybe that'll work out.

The thing about something like stackexchange, is that the students are the ones asking the questions.

That has never taken off here. Whenever I've tried to open out to Q&A posts it's always those big tricky questions - black holes, infinity, speed of light blah blah - all interesting but way beyond what could profitably be discussed so that people are making some progress in their understanding.

Making the prizes bigger won't work - that isn't the real motivation. On Google+ I had a large group, was also on some F&cebook groups - all the motivations were to solve tricky questions, tricky at whatever level the person was.

A lot of potentially interested people are in other tags, mainly computational ones, eg #programming #coding #computing #code etc

I even got an in principle agreement to load mathjax, but wasn't on steemit, was the now defunct chainbb forum. Maths is a real PITA to write out - all those little gifs!

@quantumdeveloper Please keep these contests going three times per week. I will donate 3 STEEM to you each week. Contact me on Discord if you need to chat.

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