A Math Puzzle

Consider this interesting Math Puzzle

http://www.telegraph.co.uk/education/2016/10/19/can-you-solve-this-extremely-difficult-brain-teaser-that-has-fac/?utm_source=dlvr.it&utm_medium=twitter

I don’t like their solution (in the website). I prefer Algebra as follows:

Let’s Use Algebra:

The spikes beginning from the right (to the left) each represents the place values, y^0, y^1, y^2, y^3, y^4 and y^5 respectively.

Since only two place values (namely y^0 and y^5) have digits (2 and 3) respectively by the number of “blue balls/circles” on it, we may compute the number 731 in “Base y” as follows and solve to find the value of y:

2 (y^0) + 3 (y^5) = 731
2 (1) + 3 (y^5) = 731
3 (y^5) = 731 – 2
3 (y^5) = 729
(y^5) = 729/3
(y^5) = 243
y = (243)^(1/5)
y = (3^5)^(1/5)
y = 3

Thus, the second figure represents the number

1(3^5) + 1(3^0)
= 243 + 1
= 244 (Answer)