Problem of the Week

Take four quarters, four dimes, four nickels and four pennies and distribute the sixteen coins in a 4 × 4 grid.  Is it true that by selecting one coin from each of the four rows of the grid you can always find 41¢ worth of coins; that is, one quarter, one dime, one nickel and one penny, with each from a different row?  Please explain your answer fully.

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ã2005 Alberto L. Delgado