Five students named Fred, Gail, Henry, Iggy, and Joan are seated around a circular table in that order. To decide who goes first in a game, they play "countdown”. Henry starts by saying ' 34 ', with Iggy saying ' 33 '. If they continue to count down in their circular order, who will eventually say ' 1 '?
(A) Fred
(B) Gail
(C) Henry
(D) Iggy
(E) Joan
Five students named Fred, Gail, Henry, Iggy, and Joan are seated around a circular table in that order. To decide who goes first in a game, they play "countdown". Henry starts by saying '34', with Iggy saying ' 33 '. If they continue to count down in their circular order, who will eventually say ' 1 '?
(A) Fred
(B) Gail
(C) Henry
(D) Iggy
(E) Joan

## Solution

This is an interesting question that mathematicians usually refer to as modular arithmetic. Henry starts by saying ' 34 ' and always says the number, $34-5 n$, where $n$ is a positive integer starting at 1 . In other words, he says '34', '29', ..., '9', '4'. This implies Henry says '4', Iggy says ' 3 ', Joan says ' 2 ' and Fred says ' 1 '.

ANSWER: (A)