if you check out each number out each number's posiblities and put it into a formula, you will obtain:
for the number 2: (x is any natural number, and it's diferent for every equation)
1+ 2x
Number 3
29+30x
Number 4
19+ 20x
Number 5
9+ 10x
Number 6
29 + 30x
Number 7
69 + 70x
Number 8
39 + 40x
Number 9
89+90x
Number 10
9 + 10X
So we need a number that is equivalent to all those equations. we have:
1+2X
29+30X
19+20X
9+10X
69+70X
39+40x
89+90X
So, we go and analyse the equations who give bigger products for the smallest number of X. those are: 89+90x and 69 + 70x. Replacing one of the x for another letter (y) we get:
89+90y = 69 + 70x <=> 20 = 70x - 90y
With that, we can now replace the "x" and the "y". for that formula to work, after some calculations, I notice that the x must go for 8 + 9z and the y must go 6+7z
So, starting for the 1st, if z = 0, x=8 and y=6. we replace them in the equation
89 + 90 x 6 = 629.
However, this number doesnt exist on the equation 39+40x, so its invalid.
You keep going,
z=1; x= 17 and y = 13, the final =1259, also doesnt exist on the equation 39+40x, so its invalid.
z=2, the final is 1889, also invalid.
Then, finally, z=43 y = 6+(7x3) =27........ 89 + 90x27 = 2519; which is valid for all the equations.