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)=22p(1) = 22
p(2)=3p(2) = 3
p(3)=22p(3) = 22
p(4)=2p(4) = 2
p(5)=22p(5) = 22

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

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


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