T Shape Number Grid
if you have a ten by ten grid and you get a t shape of numbers out like this:
1-2-3
--12--
--22--
The t number is the number of the bottom of the t (22)
The t total is all the nubers in the t added together (1+2+3+12+22=40)
find the nth term (to get the t total when you are given the t number)
then do the same with a 9 by 9 and/or 11 by 11 grid and try to find the nth term to get the t total from the t number from any grid.
1-2-3
--12--
--22--
The t number is the number of the bottom of the t (22)
The t total is all the nubers in the t added together (1+2+3+12+22=40)
find the nth term (to get the t total when you are given the t number)
then do the same with a 9 by 9 and/or 11 by 11 grid and try to find the nth term to get the t total from the t number from any grid.
-- matthew hinds
Labels: SharedPuzzle
posted by ToM at
7:27 PM
18 Comments:
I dont get it
What are a nubers?
Just kidding?
Wow, I sure I could figure it out, but it would take some time.
I think I will let someone else work on it. If nobody gets by the weekend, I'll spent the time to get it.
i dont get it. how do u get numbers out of a 10x10 grid???
OK.
I'm 'T-Totally' confused :-{
This is actually maths coursework in the British Maths curriculum, the days when we had to simply worry about homework are far gone indeed.
ok, you guys dont get the question so i will explain it better
a ten by ten grid like this
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
circle numbers in the grid in a t shape like this:
(1)(2)(3) 4 5 6 7 8 9 10
11(12)13 14 15 16 17 18 19 20
21(22)23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
and so on..
so you have a t
1 2 3
12
22
the bottom of the "t" is called the t number (22)
all the numbers in the "t"add up to the t total (1+2+3+12+22=40)
now you should understand
now i want you to find the nth term to get the t total of the "t" when you are given the t number of the "t"
then do the same on a 9 by 9 and/or 11 by 11 grid and try to find out the nth term for any grid
and if you are wondering i do have the answer and i will post it when i see if anyone else gets it
the t i shown you as an example doesnt look like a t because when you post something it takes awy all the spaces exept the one in between numbers and letters and thats the same reason the firs line on the grids are smaller then the rest
I am still unclear about finding the nth term.
When the grid is 9x9 the bottom of the T is at 20 and the sum is 37.
If the grid is 11x11 then the bottom of the T is at 24 and the sum is 43.
If the grid is 3x3 then T is at 8 and the total is 19.
So you are asking if the grid is X by X then where is the T and what's the total?
Or are you asking if the T moves from place to place on the 10x10 grid(changing T) then what is the total for each place the T might be?
why do you start the T at the upper left with 1,2,3? Can the T be placed in any arbitrary position on the grid?
I didn't get an answer to my query about the what you meant, but I'll make an assumption or two.
I think you mean that different t numbers mean different postions within the grid that the big T could be placed.
For a 10x10 grid with t=22, like you first proposed, the sum of the cells making up the Big T are...
t + (t-10)+ (t-20)+(t-19)+(t-21) which gives 22+12+2+3+1 = 40.
If the big T moves on the 10x10 grid, the equation would remain the same ie. sum = 5t-70
So if t=66 then the sum=66*5-70=260
If the grid changes to 11 by 11
then you would have 5t-11-22-21-23=
5t-77... specifically if t=72 then the sum is 5*72-77 = 283.
Is that what you meant by your Post?
So if I understand your post, the solution for any position t and a grid size of G by G, the equation would be...
sum = 5t-7G
In my prev post t = 72 and G=11
the sum = 5*t-7G = 360 - 77 = 283
Here's a picture of the 11 x 11 grid with two T.
http://3.bp.blogspot.com/_gQkeSWqb63Q/SjsyDg9rRYI/AAAAAAAAAEw/ZW9946IpF_E/s1600-h/11x11grid.JPG
How did you come up with 5T-70? I understand that it does work, just not sure the process you used to work out the formula.
5T-7G sorry
How did I get 5t-7G?
It's not to hard. Study the JPG at the top of my blog...
http://ragknot.blogspot.com/
Pick a place for the T. It is composed of 5 cells, the bottom is the value of t. The sum will be equal to something less that 5t.
The amount to subtract from 5t depends on the grid size. If the grid is 10, the cell just above t is 10 less that t, the cell above that is t-20, the two cells left and right of the t-20 are t-21 and t-19. Add up the negative amount for the 4 cells, 10+20+21+19=70
As the grid increases or decreases each these last 4 values increase or decrease. The total would be 7G.
ok. all im saying is that someone has the answer but there is another three parts to the question,
ill tell u the answer and the other 3 parts on monday(uk)
You said:
Find the nth term (to get the t total when you are given the t number)
I don't know what the nth term is
because you didn't tell us what n was, unless you mean it's the total.
The answer is always
Sum = 5t-7G
for any grid.
you refered to an 11x11 and a 9x9 grid.... for these G would be 11 and 9. You didn't say what the t was for these grids. So I can only give you the simple equation.
Sum = 5t-7G
yes the nth term is 5n(n being t number)-7g(g being the length of the grid)
5n-7g
so to the other three parts of the question
find the nth term when the when the t is upside down, pointing left and pointing right
simple enough
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