An investigation into the relationship between stairs size and the value.

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An investigation into the relationship between stairs size and the value.

1st stair: 25 + 26 + 27 + 35 + 36 + 45 = 194

If we represent this 1st stair in the form of n then an algebraic formula can be created.

n+(n+1)+(n+2)+(n+10)+(n+11)+(n+20)

= 6n+44

Therefore in terms of x and y, with x being the base number and y being the total of the stair the formula would be:

y=6x+44

No matter what x is replaced by the formula (6x+44) is always applicable.

25 + 26 + 27 + 35 + 36 + 45

= 194

(6x25) + 44 = 194

26 + 27 + 28 + 36 + 37 + 46

= 200

(6x26) + 44 = 200

These stairs are only one along from each other on the same line.  This formula applies to any 3 levelled stairs anywhere on the grid no matter where it is.

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45 + 46 + 47 + 55 + 56 + 65

= 314

(6x45) + 44 = 314

78 + 79 + 80 + 88 + 89 + 98

= 512

(6x78) + 44 = 512

This formula however must be changed for a stair with a higher number of levels.  If the number of levels exceeds 3 then the formula (6x + 44) is incorrect.  A new formula must be created for the stairs with four levels or more and for those with 2 or less.

Two levels

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