(1)The numbers in the boxes of the pyramid is equal to the sum of the 2 boxes below it (except for the base boxes).
(2)Let the numbers in the bottom layer be a, b and c respectively from left to right.
Therefore, the numbers in the middle boxes will be a+b and b+c.
Therefore, the number at the top is a+2b+c.
(3)
From (2), the number on top is a+2b+c.
If we switch the numbers in the bottom row,
a, b and c will be switched.
Because a+2b+c ≠b+2a+c ... etc,
Yes, the number at the top will change.
(4)
If we are given a number to work out the greatest possiblity,
Let the numbers in the bottom layer be a, b and c respectively from left to right.
The number would be regarded as a to make its effect minimum.
Then, b and c would be the greatest number possible in the range, in this case of a single digit number , 9.
Then, from (2), the number on top is a+2b+c.
In this case, the number on top will be a+18+9=a+27
(5)
Let the top number be y.
From (2), the number on top is a+2b+c. Because 2b is even,
If the top number is even, a+c must be even,so let a=1, c=1.
Then, b=(y-2)/2= 0.5y-1.
If y is odd,
a+c is odd, so let a=1, c=2.
Then, b=(y-3)/2=0.5y - 1.5