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Anyone interested in trying a maths puzzle?

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So there are twelve integers and they have 8 combinations of 3 with the same sum, and therefore a+b+c >= 78/4 right? I don't think 20 works, but ... 'distinct' is the key word!

Comments (79)

I hated that subject
@merc ah! but I always loved it, still do
I use to say to my teacher..I'm not going to need this in the real world so how about we skip this? laugh
@merc ah, but it's my version of 'God' kenken comeon!
pssst - nerd of order 1
You have the patience..I didn't laugh
I'd say a,b,or c could be the answer, possibly squared, and it may involve the hypotenuse. Or something.
lovecanbereal
Fargo,

Add this to your list of Super Hard Questions.............





Just for the record; I do not claim to be this smart......

Available time for the Super High Range IQ Test?.....

Unlimited........


professor
the answer will be a+b+c 20,21,22 etc and abcdefghijkl all in the range I guess <25
I was just about to say I'm surprised Pat isn't here solving..On my thread I was going to send him here to beat the Americans at solving this thing laugh
lovecanbereal
Fargo, et al...

I might attack this after turbocharging myself with 2 or 3 black coffees in the morning, sometime.....


Is there any way of verifying the answer?

Can't guarantee any results though.....

wave
lovecanbereal
CS Mindbenders Anonymous Division (C.S.M.B.A)............rolling on the floor laughing
lovecanbereal
The Division isn't part of the Acronym.........professor
lovecanbereal
C.S.M.B.A (for short)....................professor
If you can justify I can verify - I am sure there are online solutions
lovecanbereal
Apparently that very high IQ test, you've got to send in to some boffins, or something....professor
re we going to use Google to cheat? laugh

I can do that laugh
lovecanbereal
That's impossible, only the boffins know the answers......professor
Is a boffin a bogan?
lovecanbereal
No, but a Boffin could be a Vegan..............professor
Now I am confused laugh
It's about as useful as knowing the exact % if natrium in a rock sample from the planet Mercury..
but I remb I once apon a time found it fun too. Me was never at THIS level thou. wine
So I discussed this problem with my young Vietnamese student, who happens t obe participating in the SASMO competitive test today.

Since the sum of the 3 angles, s, must be at least sum(1...12)/4 to be an integer, it must be 20,24,28...
To reach 20, 24 or 28, the largest digit must be at least 13 (1-13 minus 11, 7 or 3 sespectively), and not greater than 15 (20), since 1-4 are not expressible as the sum of two integers (s-a) in two ways if (s-a) < 5. Haven't solved it yet! Trying it as a graph problem, 8 nodes each with three edges summing to 20,24,28...

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We see 9,8 have limited positions
Swamie
I could square this with nails and a hammer. Ruler also needed for measurement in the tri angle. (B) is my starting area. If I was helpful framing 101. rolling on the floor laughing
whoops, that's wrong, it show 13/14 and 10 connected!
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Swamie
I still would double spike (B) and fix the said image. All I see is an image leaning to the right. A,C has one nail each .I would remove those nails and fix the said image....

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I don't have time for this , I'm developing a new set of equations that redefines fractal geometry.
@swamie nothing special about a,b,c you cannot focus on any of them, one is largest surely, but that is arbitrary. Say a is largest!
Don´t forget the theorem, If A=B and B=C then A=Cprofessor I used to give these similar problems to my dummies students.rolling on the floor laughing rolling on the floor laughing
Transivity is a given
Swamie
@ Fargo it is truly a head scratch. I was just funning it. I really would like my angles at *45 deg, which has more logic. I do like the illusion. How ever giving that this is geometry, I could go back and learn more about it. I just don't have the right answer you want.

But I can fix my illusion, and was no way disrupting you class.
transitivity
@swamie it's not really a geometry problem, rather an integer problem. 8 equations in 12 distinct integers all positive, so at least 1-12, but I think 1-12 doesn't quite fit. Needs at least 13,14,15
How about this one,
?sec³dx
Only 0,5% of my students can solve it.
An Integral
Swamie
If I had three apple and took two away, I know that I had two, and that wouldn't be one. laugh But still am hungry.
Integral of sec^3xdx? 1/2secx tanx +1/2 ln sec x +tanx+C - haha I am not surprised!!!
lovecanbereal
Hint:

The line BA is parallel to the line DE

The line CA is parallel to the line DF

professor
lovecanbereal
I think........confused
lovecanbereal
If that is the case the thing is solvable quite easily. But it is the Maths Olympiad; so it can't be that easy, can it?....dunno

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