[Math Lair] How Many Days 'Til Christmas?

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[Christmas decoration displaying the number of days until Christmas]

The Christmas decoration depicted on the left displays the number of days until Christmas. It has a space where two cubes can rest. By manipulating two cubes, each of which has a digit painted on each face, you can display the number of days before Christmas. So, if there were 0 days until Christmas, you could display a single cube showing a face of "0". If there were 17 days until Christmas, you could display one cube showing a "1", and the second cube showing a "7".

How can you select the values on each face of each cube to allow you to display as many consecutive days before Christmas as possible, and what is the earliest day you can start using the decoration?

The answer is on the answer page.

Looking for more Christmas-related puzzles? See A Christmas Dinner and Some Knotty Problems. There is also "Christmas Shopping" on our sister site, All Fun and Games.

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