Roopesh - The ice cream eater

Algebra Level 3

Roopesh went to his friends house. There he ate a lot of Ice-cream. First he started with Vanilla then Chocolate then Vanilla then Butterscotch then Vanilla. He is a mathematician and made a monic polynomial of degree 5 which gave him values of the first letter of the Ice Cream.

This is the way his polynomial proceeded :-
\(p(1) = 22\)
\(p(2) = 3\)
\(p(3) = 22\)
\(p(4) = 2\)
\(p(5) = 22\)

If the value of \(p(6) = \overline{abc}\). The first letter of the ice cream he eats would be \(a+b+c\). Which ice cream will be eat next?

Assumption: \(\overline{abc}\) represents a 3 digit number.


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