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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