Birthday

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As of tomorrow, my age will no longer be a perfect number. A perfect number is the sum of its proper divisors (the numbers that go into it, not including itself). 28 is divisible by 1,2,4,7, and 14, and 1+2+4+7+14=28. The last time my age was a perfect number, I was too young to appreciate it really (1+2+3=6) and I doubt I’ll live to see my next perfect birthday, which would be 496.

It’s been a good few years. Last year, I was a cube (27=3*3*3) something which won’t happen again until I’m nearly retired (64=4*4*4). The year before that, I was one more than a square and one less than a cube. The year before that I was square (no nasty comments about me always being square please!) 24 was exciting because it had lots of factors, and of course 23 was the last time I was prime. Tomorrow I’ll be in my prime again!

Next year’s birthday I’m struggling to see any reason to look forward to, but the year after that will be very exciting as my age in binary will be 11111, and I will be a “teenager” for the last time in hex, being 1F years old. When we were young, we sometimes had binary candles on our birthday cakes, with candles lit or unlit to represent 1s and 0s. In two years, it’ll be the last birthday I can do with just 5 candles.

Finally, some maths – when I was a teacher, more often than not each class would have a couple of pupils in it who shared a birthday. Should we be surprised by this? If you’ve never come across it before, the Birthday Problem is an interesting bit of probability theory, with a nice graph to show the probability that there will be at least two people who share a birthday for increasing sizes of group. How many people would you need to be 100% sure that there would be at least two with the same birthday?

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6 Responses to “Birthday”

  1. Stu Says:

    To be absolutely sure, you’d need 367 people. Although the chance is tiny, 366 people _could_ all have different birthdays (if one was born on Feb 29). So one more person would _have_ to match.

    Probably.

    Though looking at the wiki page, the odds in the sample range of 60 upwards would be good enough to be worth putting £5 on it!

  2. Stu Says:

    Oh yes… and Happy Birthday, too!

  3. lordhutton Says:

    I’m a prime. 64 is also a 6 thingy 2x2x2x2x2x2
    My family nearly all have March birthdays, but that is probably due to sex in June

  4. Emma Says:

    I know a headteacher who commented on the coincidence of so many members of his staff having children in May.

    I spent a year telling pupils that “I was a billion seconds in September”. It took some time before any of them decided to work it out.

  5. avenue5d Says:

    The birthday problem is so odd! In every class I’ve taught there have always been at least 2 children sharing a birthday.

  6. Birthday, again. « Alison Kiddle's NRICH blog Says:

    […] year, I blogged about turning 29 and never being perfect again. It seems I was somewhat unenthusiastic about this […]

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