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National and Regional Contests
Canada Contests
Gauss
1999 Gauss
12
12
Part of
1999 Gauss
Problems
(1)
1999 Gauss (7) #12
Source:
7/6/2011
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’?
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Henry
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Joan
<span class='latex-bold'>(A)</span>\ \text{Fred} \qquad <span class='latex-bold'>(B)</span>\ \text{Gail} \qquad <span class='latex-bold'>(C)</span>\ \text{Henry} \qquad <span class='latex-bold'>(D)</span>\ \text{Iggy} \qquad <span class='latex-bold'>(E)</span>\ \text{Joan}
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Joan
Gauss
modular arithmetic