Test for love

Algebra Level 3

Sandeep is in love, and on the valentine's day he had his own plans, he thought of presenting his love with another beautiful gift.

But his girlfriend strangely gave him a test, and said that only if he passes this test she will truly accept him as a lover, and the question was: "How many gifts did you present me in the until the kiss day?"

But he was not a world memory champion, so he couldn't remember the exact number. But he was clever enough to have made a polynomial that gives the number of gifts he presented until a given day, but he remembers only this:

p ( 1 ) = 1 p ( 2 ) = 4 p ( 3 ) = 9 p ( 4 ) = 16 p ( 5 ) = 25 p(1)=1\\p(2)=4\\p(3)=9\\p(4)=16\\p(5)=25

He remembers that it was a 5 t h 5^{th} degree polynomial with leading coefficient 2 . And we know that kiss day is the 6 t h 6^{th} day of the Valentine's week, so what is p ( 6 ) p(6) ?

This is my submission for the Valentine's day celebrations , Please upvote my comment if you like it!


The answer is 276.

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Sravanth C. by Sravanth C. , 21, India

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1 solution

Nihar Mahajan
Feb 14, 2016

Construct P ( x ) = 2 ( x − 1 ) ( x − 2 ) ( x − 3 ) ( x − 4 ) ( x − 5 ) + x 2 P(x)=2(x-1)(x-2)(x-3)(x-4)(x-5) + x^2 . So P ( 6 ) = 2 × 5 ! + 36 = 240 + 36 = 276 P(6)=2\times 5! + 36 = 240+36=\boxed{276}

4 Helpful 0 Interesting 0 Brilliant 1 Confused

Moderator note:

Simple standard solution.

Challenge taking Student note : Simple Standard Solution.

Mehul Arora - 5 years, 4 months ago

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Haha cool!

Sravanth C. - 5 years, 4 months ago

I used method of differences .

A Former Brilliant Member - 5 years, 4 months ago

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