# My 300 followers problem! (Parth and Pranjal special!)

Algebra Level 5

Two maths lovers Parth and Pranjal competed each other for the number of problems solved correctly in $$300$$ days streak at Brilliant.

Let $$a_i$$ be the number of problems solved by Parth on the $$i^{th}$$ day.

Let $$b_i$$ be the number of problems solved by Pranjal on the $$i^{th}$$ day.

Note: $$a_i , b_i$$ can be rational numbers , since there may be some questions which both may have solved partially.

The two sequences $$a_1 , a_2 , …. a_{300}$$ and $$b_1 , b_2 , … b_{300}$$ are non-decreasing . The competition was tough , and Pranjal won by $$1$$ problem.

If $$\displaystyle \sum_{i=1}^{300} a_i = 1729 ,\displaystyle \sum_{i=1}^{300} b_i = 1730$$,

What is the minimum value of $$\displaystyle 30 \sum_{i=1}^{300} a_i b_i$$?

Note: $$1729$$ (taxicab number) , $$1730$$ are two consecutive sphenic numbers.

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