If you thought you were good at maths...

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Notnek
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A school level competition for speed maths:



The speed of these kids brains is beyond what I thought was possible. For GCSE/A Level students I recommend having a go at some of these problems but don't worry if they take you minutes instead of seconds

Some highlights:

30:36 - This wasn't the fastest by a long way but I have no idea how he managed to work this out so quickly. They must practice techniques for similar questions? It took me a while to get this one - can anyone see a quick way of doing it?

And then there's Luke who is in a different league:

43:20 - No idea how he processed the information so quickly
51:28 - Must be a speed reader. You may get a bit suspicious like I was just after seeing this.

The whole final from the link above is worth watching.
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username2844924
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Spoiler:
Show



With the (a-x)^2+(b-y)^2+(c-z)^2 problem, what you have to notice is that exactly one of a-x, b-y and c-z is 1 or -1 and the others are zero. WLOG we let a-x=1 (and then multiply answer by six afterwards -- by three for (b-y)^2 or (c-z)^2 being one and by two for the possibility that a-x=-1).

We then have the following possibilities for a and x:
1, 0
2, 1
3, 2
4, 3

... and the following possibilities for b and y:
0, 0
1, 1
2, 2
3, 3
4, 4

... and the following possibilities for c and z:
0, 0
1, 1
2, 2
3, 3
4, 4

So that's 4*5*5 possibilities which is 100.

As we said, we were going to multiply by six at the end, so we have 600 possibilities. I think that's the quickest way; how did you do it?


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the bear
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(Original post by Notnek)
A school level competition for speed maths:



The speed of these kids brains is beyond what I thought was possible. For GCSE/A Level students I recommend having a go at some of these problems but don't worry if they take you minutes instead of seconds

Some highlights:

30:36 - This wasn't the fastest by a long way but I have no idea how he managed to work this out so quickly. They must practice techniques for similar questions? It took me a while to get this one - can anyone see a quick way of doing it?

And then there's Luke who is in a different league:

43:20 - No idea how he processed the information so quickly
51:28 - Must be a speed reader. You may get a bit suspicious like I was just after seeing this.

The whole final from the link above is worth watching.
what a fascinating film ! i think the last question he must have done it recently.... or just a lucky guess
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username3555092
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(Original post by the bear)
what a fascinating film ! i think the last question he must have done it recently.... or just a lucky guess
Almost certainly the former, if he skipped to "what is the digital root of 3^{2017}" and used the well known trick that the digit sum of a number divisible by 9 is also divisible by 9 repeatedly.. It's a lot more believable.

Of course, the speed he did it in is still impressive. However, I like to think the kids we have here on TSR doing the various olympiads are more impressive as this competition seems to emphasise speed and familiarity more than the creative process needed to solve an entirely unknown problem - to me it sends out wrong signals for what maths is all about. It's not about speed. You could spend weeks, months, years or even lifetimes on a good problem.
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Prasiortle
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(Original post by Notnek)
A school level competition for speed maths:



The speed of these kids brains is beyond what I thought was possible. For GCSE/A Level students I recommend having a go at some of these problems but don't worry if they take you minutes instead of seconds

Some highlights:

30:36 - This wasn't the fastest by a long way but I have no idea how he managed to work this out so quickly. They must practice techniques for similar questions? It took me a while to get this one - can anyone see a quick way of doing it?

And then there's Luke who is in a different league:

43:20 - No idea how he processed the information so quickly
51:28 - Must be a speed reader. You may get a bit suspicious like I was just after seeing this.

The whole final from the link above is worth watching.
Luke was able to get full marks on AIME (somewhere between the level of our SMC and BMO) when he was in 5th grade (our Year 6). On AoPS he's universally regarded as a legend.
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Thomazo
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(Original post by I hate maths)
Almost certainly the former, if he skipped to "what is the digital root of 3^{2017}" and used the well known trick that the digit sum of a number divisible by 9 is also divisible by 9 repeatedly.. It's a lot more believable.

Of course, the speed he did it in is still impressive. However, I like to think the kids we have here on TSR doing the various olympiads are more impressive as this competition seems to emphasise speed and familiarity more than the creative process needed to solve an entirely unknown problem - to me it sends out wrong signals for what maths is all about. It's not about speed. You could spend weeks, months, years or even lifetimes on a good problem.
This, speed is not what ’being good at maths’ is about.
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.Iqra.
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Did anyone actually bothered to watch the whole vid
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NotNotBatman
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It's quite impressive, in fact, very impressive. I don't think 43:20 was very fast, because that one was more of an obvious one.

But I don't even get how they read the questions that quickly, probably loads of practise.
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Notnek
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(Original post by Thomazo)
This, speed is not what ’being good at maths’ is about.
(Original post by I hate maths)
Almost certainly the former, if he skipped to "what is the digital root of 3^{2017}" and used the well known trick that the digit sum of a number divisible by 9 is also divisible by 9 repeatedly.. It's a lot more believable.

Of course, the speed he did it in is still impressive. However, I like to think the kids we have here on TSR doing the various olympiads are more impressive as this competition seems to emphasise speed and familiarity more than the creative process needed to solve an entirely unknown problem - to me it sends out wrong signals for what maths is all about. It's not about speed. You could spend weeks, months, years or even lifetimes on a good problem.
I was waiting for someone to say this and I agree with it. I apologise for the clickbait title

I rate Olympiad above this of course but I don’t see much of a problem with this competition. We can have speed maths as well as regular maths although this competition does feel very American! I wouldn’t be surprised if a lot of the competitors are current or future Olympiad students and I’m sure that the techniques they pick up will be useful for them so it’s not a complete waste of time. Being able to think fast is very useful in any timed maths competition.
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Notnek
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(Original post by I hate maths)
Almost certainly the former, if he skipped to "what is the digital root of 3^{2017}" and used the well known trick that the digit sum of a number divisible by 9 is also divisible by 9 repeatedly.. It's a lot more believable
I don’t think he’s seen the question before but I do think that he knows what a digital root is so skipped straight to the actual question and answered it using the trick. He must be able to speed read and process information extremely quickly.
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(Original post by Notnek)
A school level competition for speed maths:



The speed of these kids brains is beyond what I thought was possible. For GCSE/A Level students I recommend having a go at some of these problems but don't worry if they take you minutes instead of seconds

Some highlights:

30:36 - This wasn't the fastest by a long way but I have no idea how he managed to work this out so quickly. They must practice techniques for similar questions? It took me a while to get this one - can anyone see a quick way of doing it?

And then there's Luke who is in a different league:

43:20 - No idea how he processed the information so quickly
51:28 - Must be a speed reader. You may get a bit suspicious like I was just after seeing this.

The whole final from the link above is worth watching.
This is impressive.

As someone who has always been very good at mental Maths and problem solving(can do 2^30 in my head, 1073741824),I'm Autistic) I still was no where near as fast as these kids! This is very inspirational and amazing! It's just a shame that there was talking going on as well as Maths, I'd have liked to see more of these guys! Especially Luke.
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Zoqua
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(Original post by .Iqra.)
Did anyone actually bothered to watch the whole vid
I did.
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Dysf(x)al
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This may be impressive, but maths should not be a FLOPs test or a test of how quickly you can read the questions. All you have to do here is merely convince yourself of the correct answer. If it were up to me, the competition would require you to PROVE that it was the correct answer, but that would make for far less interesting TV.
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DFranklin
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(Original post by Notnek)
30:36 - This wasn't the fastest by a long way but I have no idea how he managed to work this out so quickly. They must practice techniques for similar questions? It took me a while to get this one - can anyone see a quick way of doing it?
So, for what it's worth, here's a somewhat relevant couple of paragraphs from Feynman's autobiography:

(Original post by Richard_Feynman)
We had a thing at high school called the algebra team, which consisted of five kids, and we would travel to different schools as a team and have competitions. We would sit in one row of seats and the other team would sit in another row. A teacher, who was running the contest, would take out an envelope, and on the envelope it says "fortyfive seconds." She opens it up, writes the problem on the blackboard, and says, "Go!" ** so you really have more than forty*five seconds because while she's writing you can think. Now the game was this: You have a piece of paper, and on it you can write anything, you can do anything. The only thing that counted was the answer. If the answer was "six books," you'd have to write "6," and put a big circle around it. If what was in the circle was right, you won; if it wasn't, you lost.

One thing was for sure: It was practically impossible to do the problem in any conventional, straightforward way, like putting "A is the number of red books, B is the number of blue books," grind, grind, grind, until you get "six books." That would take you fifty seconds, because the people who set up the timings on these problems had made them all a trifle short. So you had to think, "Is there a way to see it?" Sometimes you could see it in a flash, and sometimes you'd have to invent another way to do it and then do the algebra as fast as you could. It was wonderful practice, and I got better and better, and I eventually got to be the head of the team. So I learned to do algebra very quickly, and it came in handy in college. When we had a problem in calculus, I was very quick to see where it was going and to do the algebra **fast.
On the other hand, if you look at the Putnam Exam Feynman famously took in 1939, you can see how much things have moved on: It's not really even STEP difficulty by today's standards. I thought it was interesting so have created a thread for discussion:

https://www.thestudentroom.co.uk/sho....php?t=5330792

As far as this competition goes: it's frustrating the way they display the question - it seems the reveal for us is slower than the contestants see (since Luke answers before the question is even fully displayed), and also that it disappears as soon as someone tries to answer. I found it made it *much* harder to "try to compete" so to speak.

And clearly the contestants have decided it's better be quick and wrong than slow and correct. Certainly with practice you can get a lot better at "intuitive guessing", and when they come off you look like a genius.

That said, I'm sure everyone on there has perfectly legitimate mathematical skills as well. And that kind of speed practice (with a bit more emphasis on correctness) will certainly help in things like the MAT, STEP and BMO/IMO as well.
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Anonymouspsych
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(Original post by Notnek)
A school level competition for speed maths:



The speed of these kids brains is beyond what I thought was possible. For GCSE/A Level students I recommend having a go at some of these problems but don't worry if they take you minutes instead of seconds

Some highlights:

30:36 - This wasn't the fastest by a long way but I have no idea how he managed to work this out so quickly. They must practice techniques for similar questions? It took me a while to get this one - can anyone see a quick way of doing it?

And then there's Luke who is in a different league:

43:20 - No idea how he processed the information so quickly
51:28 - Must be a speed reader. You may get a bit suspicious like I was just after seeing this.

The whole final from the link above is worth watching.
I managed to only do a few that they couldn't do xD. It's very impressive how fast they can do it like some of them answer the question before I have even read the damn question lol! It obviously takes a lot of practise to do that sort of problem solving efficiently.
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laurawatt
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They seemed to take a while for question 2... i thought that was the easiest :laugh: I got it as soon as i read it!

(almost none of the others though :afraid:)
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username3832246
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Luke seems like another human calculator.
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(Original post by DFranklin)
So, for what it's worth, here's a somewhat relevant couple of paragraphs from Feynman's autobiography:



On the other hand, if you look at the Putnam Exam Feynman famously took in 1939, you can see how much things have moved on: It's not really even STEP difficulty by today's standards. I thought it was interesting so have created a thread for discussion:

https://www.thestudentroom.co.uk/sho....php?t=5330792

As far as this competition goes: it's frustrating the way they display the question - it seems the reveal for us is slower than the contestants see (since Luke answers before the question is even fully displayed), and also that it disappears as soon as someone tries to answer. I found it made it *much* harder to "try to compete" so to speak.

And clearly the contestants have decided it's better be quick and wrong than slow and correct. Certainly with practice you can get a lot better at "intuitive guessing", and when they come off you look like a genius.

That said, I'm sure everyone on there has perfectly legitimate mathematical skills as well. And that kind of speed practice (with a bit more emphasis on correctness) will certainly help in things like the MAT, STEP and BMO/IMO as well.
I'm not sure how much this sort of speed practice is correlated with being good at BMO/ IMO. At the Trinity camp this year, ironically during the team relay competition (mainly focused on speed), the team with 3/8 of the IMO squad came last...
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I got question 2 before them. waay before them. and they were taking so long over it that I thought I must be wrong and it's some kind of trick question lol

it was easy.
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Notnek
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(Original post by laurawatt)
They seemed to take a while for question 2... i thought that was the easiest :laugh: I got it as soon as i read it!
Yes it was strange that they took so long for that one. I think they both thought it couldn't be that easy and as time went on, the other person not answering made them even more paranoid
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