First Patterns

I had been wondering when I would make my first post about Katie’s younger sister Zoe.  Just like I generally do with Katie, I decided that I would wait until I got inspired by something Zoe did.  And so, about a week ago, she did something sufficiently amusing and mathematical that I had the urge to write about it.

Zoe has been saying the words for the first few numbers for some time now, but recently I realized that she now knows the words for all the numbers one through twelve.  At any given time, however, she will only say a random subset, but always in the correct order.

At the particular event of interest, Zoe and I were playing with some plastic bowls.  She knows that the strange sequence of words is often said while pointing to objects, so she decided she would do the same.  The pointing was somewhat arbitrary, and sometimes the same bowl would be pointed at twice.  What amused me, however, was the sequence of numbers that she chose.  It went, “one, two, four, five, seven, eight, ten.”  Was it random coincidence, or did she know about patterns?  And what did those multiples of three ever do to her anyway?

Of course it is more fun to think that it was all carefully thought out, but I came up with the following, perhaps more probable, explanation.  First, she really likes the Russian word for four so she often skips three to get there faster.  Second, the Russian word for six starts with the nasty ‘sh’ sound that she can’t pronounce, and so she rarely says that one.  And finally, nine and ten sound so similar that at any given time she feels the need to say only one of them – this time ten happened to be the lucky one.