# Number Stairs (urgent)

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16 years ago
#61
Um. I just handed mine in today.

The end formula I got to work out the totals for ANY size step stair on ANY size grid is:

(s(s+1)/n) + G+1/6 x s cubed - G+1/6 x s

s = width of stair
G = grid size
n= keystone OR the bottom left-hand number ( same thing)

The formula above follows the patter xn+y, which is what the pattern should have been for 3 step stairs (6n+44), 4 step stairs etc on a 10x10 grid.

I worked it out by using CUBIC SEQUENCES;

an3 + bn2 + cn + d

a,b,c,d = any number
3 = cubed
2 = squared

INSTEAD, however, the n should be replaced by s (width of stair)

Then you do what you would normally do for quadratic sequences. I hope that has helped. If not. I'm sorry.
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16 years ago
#62
Could someone please explain to me how the second part of the formular works:

(g+1)/6 (x-1) (x+1) (x)

I've tried it and it works just fine, I've even developed it further adding rotation as well, but it's just that little bit I don't get, how was this part discovered how does it work?

Thanks.
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16 years ago
#63
x(x+1)/2n + x(x-1)(x+1)/6 (g+1) = T

x= height of stairs
n= bottom left hand number in staor
g= height of grid
T= total
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16 years ago
#64
U lot really r dumb...u can't explain it properly and non of u seem 2 be doing all af it
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16 years ago
#65
(((X2 + X)/2)Y) + (((X3 - X)/6)W) + ((X2 - X)/6) = T

X= width of stair
Y= bottom left hand number
W= width of number grid
T= total of number stair
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16 years ago
#66
Hi everyone,

i have just been looking thru everyone's answers and most of u hav same fomulas but i cant understand what it means. i'm getting so stuck with trying to work out which is the correct formula for the part2 of our investigation on finding a formula for any size grid for any number stair. My teacher says that if we want to do well on this we need to find this formula and be able to show that it works, now its ok having the fomrula but which one is correct for part 2 and can anyone explain it to me?
this is doing my head in, please if anyone is out there can u do me a hugh favour, it would b much appreciated and im sure u will save me tearing my hair out!!!

from troublesome lost kid
xx
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16 years ago
#67
hi all, my number stairs coursework is due...erm well 2day! and i need as much help as i can get really! i have got the formula 6x + 44, and have worked out the formulas for other sizes stairs. i also have the formula:
0.5 x 4^2 + 0.5 x

i got this formula from the internet and although i understand it, i need to show how i worked it out in my coursework. if anyone knows how this formula was worked out, plz tell me now!!!!!

xoxoxox
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16 years ago
#68
Ur all dumb arsses, this coursework is so easy!!! neway gd luck! LOL
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16 years ago
#69
lol i got this course work now!! i dont get it what you people on about what is N? no one tells me what is N? also can some one please post there eassy here thanks
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16 years ago
#70
can sum1 plz hlp me.
i need 2 know how u find da formula 4 da 3rd diffenrence
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16 years ago
#71
HAS ANY1 found de formula for part 2 can u write it out and explain it, i ave to hand it in in 4 days!!
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16 years ago
#72
tell us den or just give us a clue pleezzzz
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16 years ago
#73
(Original post by Unregistered)
wgats the formula for ne stap stair on a 10x10 grid. i really need this soon
yea the formula 4 ne step stair on a 10x10 grid is : 6s+4g-4
where s is the s-number and g means grid size! good luck!
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16 years ago
#74
can some one please expain all this i need to hand it in today!
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16 years ago
#75
S = Stair size , eg a 3x3 stair s=3
G = Grid size , eg a 10x10 grid=10
A = Amount of 'n'
N= bottom left hand corner of shape
in 2 steps :

1) (Sx(S+1)/2)= A

can some do one for me so i can understand... i tried it out for 3 squar and it wont work the answear i get is 333
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16 years ago
#76
I know that its really unlikely that anyne will read this but....

for a three step stair i got the general formula for any size grid as : 6n +4g(+4)

for a four step stair i got the general formula for any size grid as: 10n +10g(+10)

for a five step stair i got the general formula for any size grid as:15 n +20g(+20) g=grid size n=first bottom number.

they all seem to work but i now hav to find a general formula for any size stair on any size grid...and i dont know how to.basically this is in tomorrow but i can probably get away with givin it in late,so any help would be great.
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16 years ago
#77
(Original post by Unregistered)
THAT ABOVE IS RIGHT WITH A /6 ON THE END

Thanks i knw tht the formula works T=(1/2S(S+1))N+((S-1)(S+1)(S)/6)G+(S-1)(S+1)(S)/6
but how did u get it plz tell me the method or show me plz.

thnkx bye
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16 years ago
#78
(Original post by Unregistered)
THAT ABOVE IS RIGHT WITH A /6 ON THE END

hi . thnkx for the formula it works T=(1/2S(S+1))N+((S-1)(S+1)(S)/6)G+(S-1)(S+1)(S) but could u plz show me how u got it or just tell me the method but i would be more gratefull if u showed me

thnkx bye
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16 years ago
#79
(Original post by dave)
Does anybody know how to do part 2 of this. I can't find a formula that includes stair number and stair size?

11/6 s cubed + 1/2 s squared - 4/3 s + (n-1) multiplied by the formula for triangular numbers which is in the front of the maths revision guide
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16 years ago
#80
i tried all the formulas on this page and none of them worked 4 me, however, some people did have parts of the formula right so i ended up having to find the right bits and putting them together, so this is the formula which you can work out any step size on any size grid.

X(X+1)\2 + (G+1)\6 (X-1)(X+1)(X) = St

X = number of steps
G = grid size, eg, 10x10 means G is 10, 9x9 means G is 9
St = Stair total

and the \2 means divide by 2, and \6 means divide by 6

hope this helps
tom
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