Thread: How to fill in this table?

Hope it belongs to the right section....Following is a table.Here is the question:
Fill in the remaining areas by real no.s such that the sum of the numbers in any three neighboring squares is constant and sum of all no.s is 210.

|_|_|26|_|_|_|12|_|_|_|

Is it only by trial & error?
Sorry,dont know how to make tables

Originally Posted by anshulbshah

Hope it belongs to the right section....Following is a table.Here is the question:
Fill in the remaining areas by real no.s such that the sum of the numbers in any three neighboring squares is constant and sum of all no.s is 210.

|_|_|26|_|_|_|12|_|_|_|

Is it only by trial & error?
Sorry,dont know how to make tables

Filling in the blanks:
.a.b.26.c.d.e.12.f.g.h.

Resulting equations:
a+b+26 = x
b+26+c=x
26+c+d=x
c+d+e=x
d+e+12=x
e+12+f=x
12+f+g=x
f+g+h=x
a+b+26+c+d+e+12+f+g+h = 210

You have nine equations and nine unknowns.

There are several ways to attack this:

You can remove the x by subtracting the adjoining pairs.

a+b+26 = x
b+26+c=x
a - c = 0

26+c+d=x
c+d+e=x
26 - e =0

d+e+12=x
e+12+f=x
d - f =0

12+f+g=x
f+g+h=x
12 - h = 0

That's a start.
and continue with every other equation
a+b+26 = x
26+c+d=x
a+b = c+d

26+c+d=x
d+e+12=x
26+c = e +12

etc..

Or create an augmented matrix and reduce to a triangular matrix.

Hello, anshulbshah!

Fill in the remaining cells with real nnumbers
so that the sum of three consecutive numbers is constant
and sum of all numbers is 210.

. .

We are given: .

We have: .
We have: .
We have: .
. . Hence: .

Answer (so far): .


We have: .
We have: .
. . Hence: .

Answer (so far): .


We have: .
We have: .
. . Hence: .


The sum of all numbers is 210.

. .

. .

Since , we have: .

. . Hence: .


Answer: .