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Simplify your family life using modular arithmetic

For a long time, we had a big problem at dinner every night.  For some reason, none of the kids wanted to sit next to Michael and they all wanted to sit next to me.  Besides the fact that I don't have 3 sides, this made Michael feel unwanted (sniff!).  The problem was, when I chose someone to sit next to Michael the various people involved decided that I wasn't being fair, that I had chosen them last night, or last night but 2, and that Luke always got to sit next to me...  There was no way to decide.

I remembered from kindergarten that the teacher had a list of the students on the wall and would move a marker down to choose a "person of the day."  The kids knew when their turn was coming up by how many names were between themselves and the marker.  I didn't have the energy to make a list or to keep up with moving a marker, but then I realized that the dates of the month will keep up with themselves and I don't have to do anything.

So if the day of the month is evenly divisible by 3, Eleanor gets to be the person of the day.  If there is a remainder of 1, Amanda is, and if there is a remainder of 2, Luke is.  No problem, no arguments, and math is always right.  0mod3 means Ella, 1mod3 means Amanda and 2mod3 means Luke.

You can use modular arithmetic for other things, too.  Who chooses what to watch on TV? the person of the day.  Who has to practice first?  the person of the day.  When there are only two choices (for who went first at violin lessons, for example) we could use even/odd dates---the oldest child is always 0.  We use mod 5 when the whole family is involved in being chosen.

This system does have some problems.  When we have a 31 day month, Amanda is person of the day twice in a row.  But since there are drawbacks as well as benefits to being person of the day, it seems to work out.  Sometimes I am gone---Eleanor complained that I was always gone for her day to sit next to me!  But that works out in the end too, since my absences are truly random.

The best part is that while you can argue with your mother, you cannot argue with mathematics.  And arguments were exactly what I was trying to avoid.


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