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October 13–October 19, 2009

Problem

Five friends host a wine party. At the end, they are left with 45 bottles of wine, of which 9 each are full, three-quarters full, half-full, one-quarter full, and empty.

The friends wish to divide the remaining wine and the bottles, without transferring wine into different bottles, so that (1) each receives the same amount of wine (2) each receives the same number of bottles (3) each receive at least one of each kind of bottle, and (4) no two of them receive the same number of every kind of bottle.

Can you find how to distribute the bottles of wine?

Solution

here.

List of solvers

Han-Chi Fung (high school); Cezanne Camacho, Mary LaBissoniere, Matt Inouye, Jonathan Shi, Eric Scott Hughes, Huy Hoang-Nguyen, Eui Min Jung, (undergrad); Ian Johnson (graduate); Lincoln Atkinson, Wiley Young, Alex Esibov, Qiyuan Wei, Congpa You, Jake Bryant, Steve Wilmarth, T.R.Mukundan, Francesca Renouard, Najwa E., Lloyd Sakazaki, Roman Holenstein, Mike Goodman, Nellie Fung (outside).

Jonathan Shi wins the prize!