Mathemagical understanding

[andrewducker]

I'm wondering about the level of mathematical understanding on my friends list.

Go here and check out both the magical puzzle and my explanation.

Then come back here and tell me if my explanation made sense to you.

[Poll #943968]

Comments

[yalovetz]

Somewhere between the first two answers for me. I could have worked it out, but it probably would have taken me a while of figuring, so I wouldn't say it's a trivial puzzle for me.

[draconid.livejournal.com]

Ditto. I'd also have to be bothered to work it out - which generally wouldn't be the case!

[aberbotimue.livejournal.com]

ditto.. not trivial, but would ahve figured it quite quickly

but would have explained it slightly differently, as the algebra for a lot of people is just as confusing as the puzzle.

[pickwick.livejournal.com]

Roughly the same for me. I wouldn't have gone for the algebraic route, but I spotted that the answer was always a multiple of nine and that the symbols moved.

[cx650.livejournal.com]

WTF?

It sent me here:

http://www.w3.org/Protocols/

[andrewducker]

Broken link! Fixed now!

[cx650.livejournal.com]

What he said. LOL!

[despotliz.livejournal.com]

I worked it out without too much trouble but only when I noticed the symbols changing each time, and it would have taken a bit longer for me to put it down algebraically instead of in words.

[wychwood]

I said "trivial", but it's probably actually somewhere between that and the next one; I would not immediately have come to the realisation that the number "xy" was the same as "10x+y", but I'm fairly confident that I'd have figured it out eventually. The rest of the puzzle was trivial.

[wychwood]

- and I knew it was a trick and that all the possible answers would have the same symbol (naturally). If I'd looked to see which numbers had the symbol, I'd have worked it out more quickly.

[dougs.livejournal.com]

I'm very familiar with this behaviour in another context, so I knew instantly what was going on when eyeliner297 called me over to look at the page. So even the first answer is a little inaccurate.

[andrewducker]

Doesn't surprise me. I find the same thing with many logic puzzles. People ask me and then sometimes I know the answer because I've heard it three times before, which means I can come out with it instantly, making me look much smarter than I really am :->

[chipuni.livejournal.com]

*ding*

The same for me. Since I've seen (better) versions of this puzzle, this one in particular was easy to spot.

[ekatarina.livejournal.com]

I know the game and several variations on it. It was used in a Bryan Adams video a number of years ago so that the animal you thought of would "miraculously" appear on screen.

IIRC: after the initial game,

x minus 5 (always 4), then what letter does that rep in the alphabet(D), think of a country that starts with that letter(Denmark), take the second letter of that country(e), think of an animal that begins with that letter(elephant - most common response), and then we see a shot of Bryan walking down a street with an elephant.

But then again, I didn't sleep well last night

Ekatarina

[ipslore.livejournal.com]

To clarify: I worked out that the answer would be 9x, and that all of those numbers had the same symbol, but didn't notice the symbols changing each round.

[thadrin.livejournal.com]

I understood your explanation without trouble. I didn't notice the symbols shifting. I probably would eventually noticed the symbol pattern and maybe worked it out backwards. I don't know...I'm somewhere between option 1 and 2, though if I'm honest closer to 2, which I voted for.

And I have a "C" in A level maths...

[wordofblake.livejournal.com]

It is always nine!

[sterlingspider.livejournal.com]

Kindly disregard my last post as I am a spaz.

[neferet.livejournal.com]

This puzzle did the rounds in the office just before xmas. It was actually the changing symbols that got me; then I saw the pattern in the symbols, which pointed me to the solution. Bit backwards, I know :)

[loveandgarbage.livejournal.com]

I didn't notice the changing symbols initially, but noted that each number that I was left with was a multiple of 9. So I'm somewhere between a and b. The algebraic solution was elegant (as most algebraic solutions are to a lawyer).

[cangetmad.livejournal.com]

I didn't solve it algebraically, but I did extrapolate the possible solutions and see the changing symbols. So, I found a solution trivial to find, plus, yes, I understood your algebraic one.

[davidcook.livejournal.com]

My rough thought process: Ok, I pick 42. Hey, wait, let's see if I can have 42 as my number after the subtraction - worked out that nope, everything seems to go to 45 - and a lightbulb went off. Then noticed that 0 and 9 had the same symbol as 45, and that was it ...

(pedantic note: It might have been better to link first to the puzzle, then the explanation, to give people more of a chance to "solve" the puzzle unspoiled, as it were (I caught a glimpse of your explanation on my way to the puzzle, so I chose the approach above knowing that I could use the forcealgebra if all else failed :-) ))

[pickwick.livejournal.com]

I chose 42 first too :D I wonder how many people did...

[thishardenedarm.livejournal.com]

the trick in the puzzle is less to do with the math than it is to do with our perceptual bias, we are innately "blind" to the the symbols changing designation

there are a lot of puzzles based on this, all based on the same mechanism: if you present a scene/symbol/picture/array etc, then blank it out (screen image), then re-present it, we are perceptually wired to percieve it as unchanged even when major parts of it have changed...its uncanny

"change blindness" is what the psychologists call it, try googling it, or go to this for an online demo:

http://www.usd.edu/psyc301/ChangeBlindness.htm

[andrewducker]

I was mostly interested if people could follow the maths. It seemed trivial to me, but I know that a lot of people find even simple algebra impossible.

[darkoshi]

Someone previously asked me to explain that same puzzle to them, and my explanation was just about the same as yours:

You have a 2 digit number, say XY = (X * 10) + Y

You add the digits together, so X + Y

Then you subtract that from the original number,
so (X * 10) + Y - (X + Y)
= (X * 10) + Y - X - Y
= (X * 10) - X
= X * 9

So you end up with a multiple of 9.

If you look at the symbols, you'll notice that all the multiples of 9 up to 81 have the same symbol (and 81 is the max value you could have had, since X had to be between 0 and 9).

Each time you re-take the test, they switch the symbols around, but the multiples of 9 still always are given the same symbol, and that's the one the gopher shows you at the end.

[blackmanxy.livejournal.com]

My gf showed that to me a few weeks ago. Since I knew it had to be a trick, I just set about figuring it out, not with any sort of maths, but just seeing how the results would always work out to a number attached to a particular symbol.

[blackmanxy.livejournal.com]

This, incidentally, describes my entire career in math throughout school. That is, I can almost always get the right answer, but I frequently can't show you how I got there. Needless to say, I didn't do well in the "show your work"-oriented grading system I was subjected to all those years.

[moniqueleigh]

Heh. Same here. My Algebra II teacher hated me for that very reason. I always had the right answers, but my work was always goofy -- I'd get the answer, and then try to solve backwards for the "show your work" portion. It never failed, but I'd write something backwards, or take the long way 'round to get there, or something else completely idiotic. (Generally, something that would have me kicking myself over later.)

[rahaeli.livejournal.com]

I am dyscalculaic and math-deprived -- I needed a calculator to do the necessary additions and subtractions -- but I'm very very good at recognizing patterns, and I worked out something much like your solution without the algebra (I went systematically through the 40-50 series and noticed, hey, look, they're all the same answer, but the symbol's changing).

[surliminal.livejournal.com]

Like V said. I found the maths trivial but was wondering how the symbol worked for a multiple of 9 every time.

[azalemeth.livejournal.com]

Their choice of symbols is quite weird actually. And looking at the grid, you do notice the same one at every multiple of nine :-). Your explanation was correct too. Regarding the original question, I'm actually embarrassed to say that I found out on thursday that I had been awarded 100% in my most recent further-maths exam....

[soon_lee]

Was tripped up by the changing symbols which I didn't spot, but otherwise would have worked it out myself, so it's option two for me.