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# Maths question watch

1. (Original post by ZJuwelH)
So no one's got it yet? Hope Hayden comes out with it tomorrow, I'd love to see it.

Sod it, economics for me now. Damn I should've done that in the first place, might have got into Cambridge!
i dont think theres going to be an answer from hayden, it has been up since december.
2. Assume such a factorisation did exist such that:

x^2 + y^2 + z^2 = (ax + by + cz)(dx + ey + fz).

=> ad = be = cf = 1 and (ae+bd) = (bf+ce) = (af+cd) = 0.

=> (ae+bd)(bf+ce)(af+cd) = 0

=> (aebf + ace^2 + b^2df + bdce)(af+cd) = 0

=> a^2f^2be + a^2e^2cf + b^2d^2fc +b^2f^2ad + e^2c^2ad + c^2d^2be + 2abcdef = 0

=> a^2(f^2+e^2) + b^2(d^2+f^2) + c^2(e^2+d^2) + 2abcdef = 0.

But e^2 + f^2 = d^2 + f^2 = d^2 + e^2 = 0.

=> 2abcdef = 0. So one of a,b,c,d,e,f is 0. Contradiction.
3. (Original post by theone)
=> ad = be = cf = 1 and (ae+bd) = (bf+ce) = (af+cd) = 0.
just correcting you

i was going to go down the matrix route.
4. (Original post by elpaw)
i dont think theres going to be an answer from hayden, it has been up since december.
Oh. Didn't see that. Lazy cad, imagine when he sees this and thinks "Oh yeah"!
5. (Original post by elpaw)
just correcting you

i was going to go down the matrix route.
Cheers .
6. (Original post by theone)
Cheers .
its ok. the matrix route was going nowhere, unless i proved that d, e, and f had to be both positive and negative at the same time.
7. (Original post by rahaydenuk)
Great solution
8. In richard's likeness, I'll post another problem, which is nowhere near as hard:

"The village of wonder-upon-the-wye has an annual tennis tournament. This year a record number of participants have entered. These participants were grouped into various leagues, with the same amount of competitors in each league. In each league, every player played every other played exactly once. However, it was found that this meant there were too many games to be played. So the number of groups was the increased by 1, and once again there was the same number of competitors in each group. This reduced the number of games by 55. How many competitors are there?"
9. (Original post by theone)
In richard's likeness, I'll post another problem, which is nowhere near as hard:

"The village of wonder-upon-the-wye has an annual tennis tournament. This year a record number of participants have entered. These participants were grouped into various leagues, with the same amount of competitors in each league. In each league, every player played every other played exactly once. However, it was found that this meant there were too many games to be played. So the number of groups was the increased by 1, and once again there was the same number of competitors in each group. This reduced the number of games by 55. How many competitors are there?"
is the village name important?

i hate factorials....
10. (Original post by elpaw)
is the village name important?
Of course!!
11. (Original post by bono)
Of course!!
I actually made it up myself, so yes!
12. (Original post by theone)
I actually made it up myself, so yes!
theone, I just wanted to ask, would you need knowledge in AS Level statistics to do this question? e.g.) S1, S2?
13. (Original post by theone)
In richard's likeness, I'll post another problem, which is nowhere near as hard:

"The village of wonder-upon-the-wye has an annual tennis tournament. This year a record number of participants have entered. These participants were grouped into various leagues, with the same amount of competitors in each league. In each league, every player played every other played exactly once. However, it was found that this meant there were too many games to be played. So the number of groups was the increased by 1, and once again there was the same number of competitors in each group. This reduced the number of games by 55. How many competitors are there?"
reduced number of games by 55 per league or in total?
14. Bono, you may need a teeny bit of S2, bit you don't have to, you should be able to work it out yourself (hint: You can use nCr, which is the number of distinct subsets of size r chosen from a larger subset of size n).

lgs98jonee, Overall number of games.
15. Sounds more like pure maths to me bono.
16. (Original post by theone)
Bono, you may need a teeny bit of S2, bit you don't have to, you should be able to work it out yourself (hint: You can use nCr, which is the number of distinct subsets of size r chosen from a larger subset of size n).

lgs98jonee, Overall number of games.
I don't do stats, only mechanics

*feels rejected as cannot attempt question*
17. is it just the first round of the tournament, or does it go into quarter-finals, semis, etc?
18. (Original post by theone)
Bono, you may need a teeny bit of S2, bit you don't have to, you should be able to work it out yourself (hint: You can use nCr, which is the number of distinct subsets of size r chosen from a larger subset of size n).

lgs98jonee, Overall number of games.
surely number of games played = no of teams -1 *no of teams /2???
19. (Original post by XTinaA)
Sounds more like pure maths to me bono.
But you would need a sort of nth term formula to calculate the number of games played per group, depending on the number of players in that group.

That would be the first step?
20. (Original post by bono)
I don't do stats, only mechanics

*feels rejected as cannot attempt question*
i havent used any stats to do q

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