Math Olympiad Question with @ThePhysicsMathsWizard

Denis from @ThePhysicsMathsWizard challenges me with a question from the Vietnam Math Olympiad about the floor function... #tomrocksmaths #thephysicsmathswizard

The question asks for all positive solutions to the equation 0.9t = floor(t) / (t - floor(t)). My approach was to first rule out integer solutions and then solve for t in the range (n, n+1). This leads to a quadratic equation and a series of inequalities that need to be satisfied for the solutions to be valid.

Get your Tom Rocks Maths merchandise here:

[ThePhysicsMathsWizard]

Great job Tom, am glad for working with you on this one, I like the way you solved the problem and the thought process. Cheers

[boualemhabib]

Humility is so intrinsic to your nature that I truly believe that many people didn't think that you already knew the solution to the equation as soon as it was within your eyesight. I have followed you on youtube for a while. I enjoyed your 125 miles self inflicted torture run. As the french would say, de la folie pure.Tout mon respect.
you are a true teacher. Chapeau.

[susie]

Wow, I wasn't expecting to find a maths video so interesting! It'd be really cool if you could do some videos on similar questions, and how you can practise to improve your problem solving skills! I'm an alevel (further) maths student and although I find the class content fine, I struggle with things like the senior maths challenge as I just can't think straight to a solution haha

[shivashankar]

Amazing prof, haven't learnt this as an undergraduate in Electrical Engineering, but pretty cool !

[domc]

I love how everything follows logically (i.e no magic tricks) really great stuff Tom

[phenixorbitall]

Great :) It is a cool mixture of nerdyness and useful entertainment. Watching both of you doing maths feels like listening to two musicians embarking on some intense jazzy maths improvisation - pretty cool. It made me smile at the end :) Please continue collaborating together!

[TwisterX]

I've done it in the same way hahaha, the only diference is that a called t = n + e, where n is an integer and 'e' is a numbem between 0 and 1. So in the end what changed was the condition that would filter the values of n.

[RobertSmith]

Moreover, to see why the first t doesnt work, it is easy to see from the expression (with negative radical) that t < n/2, which contradicts the fact that t >n

[floreaciprian]

These videos are so much fun to watch. We get to meet other youtubers passionate about maths, we see both sides challanged, we see the thought process both. This idea to involve other people was just brilliant. Thanks and i hope we get to see more

[nuranichandra]

Admire the fantastic problem and solution strategy

[babagaming]

Woooo this collaboration was nice the number is so cool. I knew this channel from math physics wizard but their is also good content. Yap guys keep on keeping on

[rijulbarot]

Hey, I found a method free of the quadratic complications, so I thought id share it. Write the greatest integer t to be x, and then t - x = f, ( f for fraction :D and it goes from (0, 1)), so the equation becomes 0.9(x+f) = x/f, which implies 0.9(x+f) > x, so x < 9f and from the range of f we get the possible values of x to be 1, 2, 3, 4, 5, 6, 7, 8. Cheers and great video btw!

[CommanderdMtllca]

Do more like this!!! I love seeing math videos where someone has to think out loud instead of guiding the video with a scripted solution.

[abbe]

Great video! Make more videos like this, were you try to solve problems live. It's really interesting.

[RobertSmith]

you can show immediately that n is less than 9 as follows, :
From the equation you get that t - n = n / (0.9 t) which should be less than 1, This implies that 10n < 9t. But t <n+1. So, we have 10n < 9(n+1) and so n <9. Then solve quadratically for t as you did.

[rehab]

Never seen a mathematician with the drip that this man has

[desertstorm]

I like how doctor aproaches every problem.
Also i like how innocent this guy looks. wow 🥰

[iteerrex]

Seemingly simple but a tricky little problem. Nicely done professor.

[nDreaw]

Damn I feel so dumb by this Video but still love it and appreciate all ur Vids Tom 👌

[parkie]

God this was such a fun problem. Gonna go look at the vietnamese math olympiad lmao