I am a Math Geek
Wednesday, July 9, 2008

It's true, I confess.  On Sunday, we played Mexican Train with my aunt and uncle, which is a game of dominoes.  Mexican Train uses a set of "double twelve" dominoes (I think that's the minimum; their set went up to 15).  At home, I have a set of "double six" dominoes, but I remembered seeing in my set the hexagonal centerpiece similar to the one used in Mexican Train.  So today I played a miniature game of Mexican Train with my mom, using what pieces we had available.  It was a very short game.  Curious, I felt compelled to calculate the mathematical formula that describes how many dominoes belong to a set.

If anyone cares (and I can't imagine who would), the formula is:

where n represents the greatest number of spots in the set.  So a set that goes up to six spots contains 28 dominoes (1+2+3+4+5+6+7), and a set with twelve spots has 91 pieces.

If you're wondering why it's n+1 instead of just n, it's because dominoes have "blanks" (zeros).

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The Spirit of the Lord God is upon Me,
because the Lord has anointed Me
to preach good tidings to the poor;
He has sent Me to heal the brokenhearted,
to proclaim liberty to the captives
and release from prison to those who are bound;
to proclaim the acceptable year of the Lord,
and the day of vengeance of our God;
to comfort all who mourn,
to console those who mourn in Zion,
to give them beauty for ashes,
the oil of joy for mourning,
the garment of praise for the spirit of heaviness;
that they may be called trees of righteousness,
the planting of the Lord, that He may be glorified.
— Isaiah 61:1-3