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by Chris Burke
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942: It's All About The Year, The New Year ... 2015!
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Mr. Michael Keegan, Math Teacher

And you know that he probably does, too.

The new year, 2015, brings some interesting numbers when converted into other bases. Granted, I find most numbers interesting in some way, but these still have interesting features.

In base 2 (binary), we have a palindrome; it's the same backward. The 0 in the middle means that we are 32 years away from all 1s and 33 away from rolling over the counter and adding another digit.

In base 3 (trinary), the number can be broken down into 2 20 21 22, which is somewhat sequential.

In base 4 (tetranary(?), ah skip it!), which is related to base 2 by virtue of being a power of 2, we get 133 133. It's not the palindrome that base 2 is; it's something more fun!

I don't have much to say about bases 5, 6, or 7. They have pairs of numbers, but that's hardly surprising. Two of them look like zip codes, so I checked: 31030 is Fort Valley, Georgia and 13155 in an area of upstate New York, south of Syracuse. (I thought it might be a section of Queens, in New York City, which is why I checked. Nope.) Last year, base 5 was 31024, which had all five available numbers in it, but we're a year too late for that.

In base 8 (octal), another power of 2, we get another repetition: 3737. Wonderful.

In base 9, meh. I hope everyone could figure out what base 10 was, so I skipped it. Base 11 likewise is boring as no alphabetic characters were required to substitute for numbers greater than 9.

In base 12, it gets interesting. While 12 is a multiple of 2, it isn't a power of 2. Using alphabetic characters, it's 11BB, but the "B" is a stand in for 11, so it's actually 1,1,11,11. Practically binary! (But it's not.) Note: in bases larger than 10, such as Sexagesimal, it is common to write the numbers in decimal form (no letters) and separate the powers with commas.

In base 13, we have 11, 12, 0 because the year is divisible by 13. Last year was 11, 11, 12. The year before 11, 11, 11. (You see: there's always something to be found!)

Finishing up, in base 14, 10 and 3 make 13. And we end with snoozy bases 15 and 16 (hexadecimal), which aren't all that interesting this year, although next year is 7E0 or 7, 14, 0. Something to look forward to!


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